Deck 9: Random Variables and Statistics

Question 1

Suppose X is a normal random variable with $\mu = 340$ and $\sigma = 20$ . Find the value of $P ( 360 \leq X \leq 370 )$ . Please, round the answer to four decimal places.

A) $P ( 360 \leq X \leq 370 ) = 0.0668$
B) $P ( 360 \leq X \leq 370 ) = 0.9332$
C) $P ( 360 \leq X \leq 370 ) = 0.0929$
D) $P ( 360 \leq X \leq 370 ) = 0.0919$
E) $P ( 360 \leq X \leq 370 ) = 0.1587$

Answer 1

$P ( 360 \leq X \leq 370 ) = 0.0919$

Question 2

If you roll a die 300 times, what is the probability that you will roll between 50 and 60 fives (Round your answer to two decimal places.) ?

A)0.24
B) 0.47
C) 0.52
D) 0.48
E) 0.76

Answer 2

0.48

Question 3

This exercise is based on the following information, gathered from student testing of a statistical software package called MODSTAT. Students were asked to complete certain tasks using the software, without any instructions. The results were as follows. (Assume that the time for each task is normally distributed.) Assuming that the time it takes a student to complete each task is independent of the others, find the probability that a student will take at least 10 minutes to complete each of Tasks 1 and 2. Round your answer to four decimal places. $\begin{array} { | l | l | l | } \hline \text { Task } & \begin{array} { l } \text { Mean Time } \\\text { (minutes) }\end{array} & \begin{array} { l } \text { Standard } \\\text { Deviation }\end{array} \\\hline \text { Task 1: Descriptive Analysis of Data } & 11.4 & 5.0 \\\hline \text { Task 2: Standardizing Scores } & 11.2 & 8.0 \\\hline \text { Task 3: Poisson Probability Table } & 7.3 & 3.9 \\\hline \text { Task 4: Areas Under Normal Curve } & 9.1 & 5.5 \\\hline\end{array}$

A)0.3425
B) 0.3405
C) 0.6595
D) 0.3415
E) 0.6585

Answer 3

0.3415

Question 4

Suppose X is a normal random variable with $\mu = 30$ and $\sigma = 10$ . Find the value of $P ( 24 \leq X \leq 46 )$ . Please, round the answer to four decimal places.

A) $P ( 24 \leq X \leq 46 ) = 0.3291$
B) $P ( 24 \leq X \leq 46 ) = 0.0548$
C) $P ( 24 \leq X \leq 46 ) = 0.7257$
D) $P ( 24 \leq X \leq 46 ) = 0.6709$
E) $P ( 24 \leq X \leq 46 ) = 0.6699$

Question 5

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. $$P ( - 1.31 < Z < 1.76 )$$
Round your answer to four decimal places.

A) $P ( - 1.31 < Z < 1.76 ) = 0.8657$
B) $P ( - 1.31 < Z < 1.76 ) = 0.0914$
C) $P ( - 1.31 < Z < 1.76 ) = 0.9608$
D) $P ( - 1.31 < Z < 1.76 ) = 0.0951$
E) $P ( - 1.31 < Z < 1.76 ) = 0.0559$

Question 6

If we model after-tax household income with a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is normal, and round all percentages to the nearest whole number. What percentage of Swedish households are either very wealthy (income at least $100,000) or very poor (income at most $12,000) Express your answer to the nearest 1%. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Country } & \text { U.S. } & \text { Canada } & \text { Switzerland } & \text { Germany } & \text { Sweden } \\\hline \begin{array} { l } \text { Mean } \\\text { household } \\\text { income }\end{array} & \$ 38,000 & \$ 35,000 & \$ 39,000 & \$ 34,000 & \$ 32,000 \\\hline \begin{array} { l } \text { Standard } \\\text { deviation }\end{array} & \$ 21,000 & \$ 17,000 & \$ 16,000 & \$ 14,000 & \$ 11,000 \\\hline\end{array}$$

A)51%
B) 3%
C) 7%
D) 6%
E) 97%

Question 7

If we model after-tax household income with a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is normal, and round all percentages to the nearest whole number. What percentage of Sweden households had an income of $50,000 or more $\begin{array} { | l | l | l | l | l | l | } \hline \text { Country } & \text { U.S. } & \text { Canada } & \text { Switzerland } & \text { Germany } & \text { Sweden } \\\hline \begin{array} { l } \text { Mean } \\\text { household } \\\text { income }\end{array} & \$ 38,000 & \$ 35,000 & \$ 39,000 & \$ 34,000 & \$ 32,000 \\\hline \begin{array} { l } \text { Standard } \\\text { deviation }\end{array} & \$ 21,000 & \$ 17,000 & \$ 16,000 & \$ 14,000 & \$ 11,000 \\\hline\end{array}$

A)22%
B) 95%
C) 4%
D) 89%
E) 5%

Question 8

Z is the standard normal distribution. Find the probability . Please, round the answer to four decimal places.
​ __________

Question 9

Z is the standard normal distribution. Find the probability $P ( - 1.6 \leq Z \leq 0 )$ . Please, round the answer to four decimal places.

A) $P ( - 1.6 \leq Z \leq 0 ) = 0.4452$
B) $P ( - 1.6 \leq Z \leq 0 ) = 0.5448$
C) $P ( - 1.6 \leq Z \leq 0 ) = 0.16$
D) $P ( - 1.6 \leq Z \leq 0 ) = 0.4552$
E) $P ( - 1.6 \leq Z \leq 0 ) = 0.5648$

Question 10

IQ scores (as measured by the Stanford-Binet intelligence test) are normally distributed with a mean of 100 and a standard deviation of 16. Find the approximate number of people in the U.S. (assuming a total population of 280,000,000) with an IQ higher than 120. ​
Round your answer to the nearest 100,000.
​

A)30,600,000 people
B) 265,200,000 people
C) 29,600,000 people
D) 250,400,000 people
E) 132,600,000 people

Question 11

The mean batting average in major league baseball is about 0.250. Supposing that batting averages are normally distributed, that the standard deviation in the averages is 0.05, and that there are 245 batters, what is the expected number of batters with an average of at least 0.400 Round your answer to two decimal places.

A)0.25 batters
B) 0.75 batters
C) 0.37 batters
D) 0.32 batters
E) 0.2 batters

Question 12

Find the probability that a normal variable takes values more than $\frac { 1 } { 4 }$ standard deviations away from its mean. Please, round the answer to four decimal places.

A)0.9867
B) 0.8026
C) 0.8016
D) 0.4013
E) 0.8036

Question 13

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. $$P ( 0.7 < Z < 1.87 )$$

Round your answer to four decimal places.

A) $P ( 0.7 < Z < 1.87 ) = 0.7273$
B) $P ( 0.7 < Z < 1.87 ) = 0.2113$
C) $P ( 0.7 < Z < 1.87 ) = 0.7580$
D) $P ( 0.7 < Z < 1.87 ) = 0.9693$
E) $P ( 0.7 < Z < 1.87 ) = 0.9414$

Question 14

Your company issues flight insurance. You charge $2 and in the event of a plane crash, you will pay out $1 million to the victim or his or her family. In 1989, the probability of a plane crashing on a single trip was 0.00000165. If ten people per flight buy insurance from you, what was your approximate probability of losing money over the course of 100 million flights in 1989 Round your answer to four decimal places. [Hint: First determine how many crashes there must be for you to lose money.] ?

A)0.9971
B) 0.0039
C) 0.136
D) 0.0029
E) 0.0019

Question 15

Suppose X is a normal random variable with $\mu = 40$ and $\sigma = 20$ . Find the value of $P ( 30 \leq X \leq 45 )$ . Please, round the answer to four decimal places.

A) $P ( 30 \leq X \leq 45 ) = 0.8549$
B) $P ( 30 \leq X \leq 45 ) = 0.2892$
C) $P ( 30 \leq X \leq 45 ) = 0.7098$
D) $P ( 30 \leq X \leq 45 ) = 0.2902$
E) $P ( 30 \leq X \leq 45 ) = 0.2912$

Question 16

The probability of a plane crashing on a single trip in 1989 was 0.00000165. Find the approximate probability that in 50,000,000 flights there will be fewer than 90 crashes. Round your answer to four decimal places. Round Z to two decimal places. ​

A)0.5332
B) 0.7804
C) 0.7784
D) 0.5342
E) 0.7794

Question 17

The new computer your business bought lists a mean time between failures of 1 year, with a standard deviation of 3 months. Eight months after a repair, it breaks down again. Is this surprising (Assume that the times between failures are normally distributed.)

A)This is not unusual.
B) This is unusual.

Question 18

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 300 and 600. Round your answer to four decimal places. ​

A)0.5907
B) 0.8185
C) 0.2954
D) 0.1815
E) 0.8175

Question 19

IQ scores as measured by both the Stanford-Binet intelligence test and the Wechsler intelligence test have a mean of 100. The standard deviation for the Stanford-Binet test is 16, while that for the Wechsler test is 14. For which test do a smaller percentage of test-takers score less than 80 ?

A)Wechsler
B) Stanford-Binet
C) Percentages are equal

Question 20

This exercise is based on the following information, gathered from student testing of a statistical software package called MODSTAT. Students were asked to complete certain tasks using the software, without any instructions. The results were as follows. (Assume that the time for each task is normally distributed.) It can be shown that if X and Y are independent normal random variables with means $\mu _ { X }$ and $\mu _ { y }$ and standard deviations $\sigma _ { X }$ and $\sigma _ { y }$ respectively, then their sum $X + Y$ is also normally distributed and has mean $\mu = \mu _ { X } + \mu _ { Y }$ and standard deviation $\sigma = \sqrt { \sigma ^ { 2 } X + \sigma ^ { 2 } Y }$ . Assuming that the time it takes a student to complete each task is independent of the others, find the probability that a student will take at least 20 minutes to complete both Tasks 3 and 4. Round your answer to four decimal places. $$\begin{array} { | l | l | l | } \hline \text { Task } & \begin{array} { l } \text { Mean Time } \\\text { (minutes) }\end{array} & \begin{array} { l } \text { Standard } \\\text { Deviation }\end{array} \\\hline \text { Task 1: Descriptive Analysis of Data } & 11.4 & 5.0 \\\hline \text { Task 2: Standardizing Scores } & 11.9 & 9.0 \\\hline \text { Task 3: Poisson Probability Table } & 7.5 & 4.1 \\\hline \text { Task 4: Areas Under Normal Curve } & 9.5 & 5.9 \\\hline\end{array}$$

A)0.3382
B) 0.6638
C) 0.6764
D) 0.3372
E) 0.6628

Question 21

Your company issues flight insurance. You charge $2 and in the event of a plane crash, you will pay out $1 million to the victim or his or her family. In 1989, the probability of a plane crashing on a single trip was 0.00000165. If ten people per flight buy insurance from you, what was your approximate probability of losing money over the course of 110 million flights in 1989 Round your answer to four decimal places. [Hint: First determine how many crashes there must be for you to lose money.]

Question 22

The mean batting average in major league baseball is about 0.250. Supposing that batting averages are normally distributed, that the standard deviation in the averages is 0.05, and that there are 250 batters, what is the expected number of batters with an average of at least 0.400 Round your answer to two decimal places.
?
The answer is __________ batters.

Question 23

Suppose X is a normal random variable with and . Find the value, rounding to four decimal places, of
​ __________

Question 24

The probability of a plane crashing on a single trip in 1989 was 0.00000165. Find the approximate probability that in 50,000,000 flights there will be fewer than 80 crashes. Round your answer to four decimal places. Round Z to two decimal places.

Question 25

Z is the standard normal distribution. Find the probability . Please, round your answer to three decimal places.
​ __________

Question 26

Compute the standard deviation of the data sample.
$- 4,3,6,9,14$
Round your answer to two decimal places if necessary.

A)6.73
B) 41.92
C) 22.9
D) 4.79
E) 6.02

Question 27

This exercise is based on the following information, gathered from student testing of a statistical software package called MODSTAT. Students were asked to complete certain tasks using the software, without any instructions. The results were as follows. (Assume that the time for each task is normally distributed.) Assuming that the time it takes a student to complete each task is independent of the others, find the probability that a student will take at least 10 minutes to complete each of Tasks 1 and 2. Round your answer to four decimal places.

Question 28

Find the probability that a normal variable takes values more than standard deviations away from its mean. Please, round the answer to three decimal places.

Question 29

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score 340 or lower. Round your answer to four decimal places.

Question 30

This exercise is based on the following information, gathered from student testing of a statistical software package called MODSTAT. Students were asked to complete certain tasks using the software, without any instructions. The results were as follows. (Assume that the time for each task is normally distributed.) It can be shown that if X and Y are independent normal random variables with means and and standard deviations and respectively, then their sum is also normally distributed and has mean and standard deviation . Assuming that the time it takes a student to complete each task is independent of the others, find the probability that a student will take at least 20 minutes to complete both Tasks 3 and 4. Round your answer to four decimal places. Round Z to two decimal places.

Question 31

Suppose X is a normal random variable with and . Find the value, rounding to four decimal places, of
​ __________

Question 32

IQ scores (as measured by the Stanford-Binet intelligence test) are normally distributed with a mean of 100 and a standard deviation of 16. Find the approximate number of people in the U.S. (assuming a total population of 280,000,000) with an IQ higher than 120.
​
Round your answer to the nearest 100,000.
​
__________ people

Question 33

X has a normal distribution with the given mean and standard deviation. Find the probability. Please, round the answer to three decimal places.
​ , ​ __________

Question 34

The population standard deviation is greater than the sample standard deviation.

Question 35

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve.
? ?
Round your answer to four decimal places.
? $P ( 0.6 \leq Z \leq 1.88 ) =$ __________

Question 36

If we model after-tax household income with a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is normal, and round all percentages to the nearest whole number. What percentage of U.S. households had an income of $50,000 or more Express your answer to the nearest 1%. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Country } & \text { U.S. } & \text { Canada } & \text { Switzerland } & \text { Germany } & \text { Sweden } \\\hline \begin{array} { l } \text { Mean } \\\text { household } \\\text { income }\end{array} & \$ 38,000 & \$ 35,000 & \$ 39,000 & \$ 34,000 & \$ 32,000 \\\hline \begin{array} { l } \text { Standard } \\\text { deviation }\end{array} & \$ 21,000 & \$ 17,000 & \$ 16,000 & \$ 14,000 & \$ 11,000 \\\hline\end{array}$$
__________% of households

Question 37

The new computer your business bought lists a mean time between failures of 1 year, with a standard deviation of 3 months. Eight months after a repair, it breaks down again. Is this surprising (Assume that the times between failures are normally distributed.)

Question 38

If you roll a die 300 times, what is the probability that you will roll between 50 and 80 sixs Please, round your answer to three decimal places.

Question 39

If we model after-tax household income with a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is normal, and round all percentages to the nearest whole number. What percentage of German households are either very wealthy (income at least $100,000) or very poor (income at most $12,000) Express your answer to the nearest 1%. $$\begin{array} { | l | l | l | l | l | l | } \hline \text { Country } & \text { U.S. } & \text { Canada } & \text { Switzerland } & \text { Germany } & \text { Sweden } \\\hline \begin{array} { l } \text { Mean } \\\text { household } \\\text { income }\end{array} & \$ 38,000 & \$ 35,000 & \$ 39,000 & \$ 34,000 & \$ 32,000 \\\hline \begin{array} { l } \text { Standard } \\\text { deviation }\end{array} & \$ 21,000 & \$ 17,000 & \$ 16,000 & \$ 14,000 & \$ 11,000 \\\hline\end{array}$$
__________% of households

Question 40

LSAT test scores are normally distributed with a mean of 500 and a standard deviation of 100. Find the probability that a randomly chosen test taker will score between 350 and 550. Round your answer to four decimal places.

Question 41

In your bid to be elected class representative, you have your election committee survey five randomly chosen students in your class and ask them to rank you on a scale of 0 - 10. Your rankings are 5, 9, 7, 2, 3.
Calculate the sample standard deviation, rounded to two decimal places.

A) $s = 4.1$
B) $s = 2.28$
C) $s = 5.2$
D) $s = 2.86$
E) $s = 8.2$

Question 42

The following list shows the percentage of aging population (residents of age 65 and older) in each of the 50 states in 1990 and 2000.
2000
$$\begin{array} { l } 6,9,10,10,10,11,11,11,11,11 , \\11,11,12,12,12,12,12,12,12,12 , \\12,12,12,13,13,13,13,13,13,13 , \\13,13,13,13,13,13,13,14,14,14 , \\14,14,14,14,15,15,15,15,16,18\end{array}$$
1990
$$\begin{array} { l } 4,9,10,10,10,10,10,11,11,11 , \\11,11,11,11,11,12,12,12,12,12 , \\12,13,13,13,13,13,13,13,13,13 , \\13,13,13,13,13,14,14,14,14,14 , \\14,14,14,15,15,15,15,15,15,18\end{array}$$
What was the actual percentage of states whose aging population in 1990 was within two standard deviations of the mean Round your answer to one decimal place if necessary.

A)96%
B) 95%
C) 97%
D) 75%
E) 86%

Question 43

Calculate the standard deviation of X for the probability distribution. $$\begin{array} { | c | c | c | c | c | } \hline x & 1 & 2 & 3 & 4 \\\hline P ( X = x ) & 0.2 & 0.3 & 0.3 & 0.2 \\\hline\end{array}$$ Round your answer to two decimal places if necessary.

A)1.05
B) 1
C) 1.02
D) 2.5
E) 5

Question 44

Which is smaller: the sample standard deviation or the population standard deviation ?

A)the population standard deviation
B) the sample standard deviation

Question 45

Your company, Sonic Video, Inc., has conducted research that shows the following probability distribution, where X is the number of video arcades in a randomly chosen city with more than 500,000 inhabitants. As CEO of Startrooper Video Unlimited, you wish to install a chain of video arcades in Sleepy City, U.S.A. The city council regulations require that the number of arcades be within the range shared by at least 75 percent of all cities. Find the largest number of video arcades you should install so as to comply with this regulation. $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | c | } \hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\\hline P ( X = x ) & 0.05 & 0.1 & 0.31 & 0.21 & 0.11 & 0.16 & 0.02 & 0.02 & 0.01 & 0.01 \\\hline\end{array}$$

A)6
B) 4
C) 5
D) 7
E) 3

Question 46

Compute the (sample) standard deviation for the data. Please round your answer to two decimal places. $5,2,5 , - 4,0,16$

A) $s = 46$
B) $s = 13.56$
C) $s = 20.34$
D) $s = 16$
E) $s = 6.78$

Question 47

Calculate the standard deviation of X for the probability distribution. Please round your answer to two decimal places, if necessary. $$\begin{array} { | c | c | c | c | c | c | c | } \hline x & - 5 & - 2 & 0 & 3 & 6 & 10 \\\hline P ( X = x ) & 0.2 & 0.3 & 0.2 & 0.1 & 0 & 0.2 \\\hline\end{array}$$

A) $\sigma = 10$
B) $\sigma = 13.31$
C) $\sigma = 0.7$
D) $\sigma = 26.61$
E) $\sigma = 5$

Question 48

Calculate the standard deviation of X for the probability distribution. $$\begin{array} { | c | c | c | c | c | } \hline x & 2 & 4 & 5 & 3 \\\hline P ( X = x ) & 0.5 & 0.1 & 0.2 & 0.2 \\\hline\end{array}$$ Round your answer to two decimal places if necessary.

A)1.25
B) 3
C) 1.4
D) 6
E) 1.18

Question 49

In some year, 21 percent of all teenagers in the U.S. had checking accounts. Your bank, TeenChex Inc., is interested in targeting teenagers who do not already have a checking account. ​
TeenChex selects a random sample of 1,000 teenagers. Find the interval in which the chance that teenagers in the sample will not have checking accounts is approximately 95 percent. Please round your answer to the nearest whole number.
​

A)764 - 790
B) 790 - 816
C) 777 - 803
D) 764 - 816
E) 790 - 803

Question 50

Calculate the standard deviation of X for the probability distribution.
Please round your answer to the nearest whole number, if necessary. ​ __________

Question 51

Following is a sample of tow ratings (in pounds) for some popular 2000 model light trucks:
3,000, 3,000, 4,000, 5,000, 6,000, 7,000, 7,000, 7,000, 9,000, 9,000

Compute the standard deviation of the given sample. Round your answer to the nearest whole number.

A) $s = 2,211$
B) $s = 6,000$
C) $s = 3,789$
D) $s = 4,422$
E) $s = 8,211$

Question 52

The following is a sample of the percentage increases in the price of a house in eight regions of the U.S.
75, 125, 160, 160, 160, 225, 225, 300

Compute the standard deviation of the given sample. Please, use the value for mean, rounded to the nearest whole number in your calculations. Round answer to the nearest whole number.

A) $s = 69$
B) $s = 248$
C) $s = 179$
D) $s = 110$
E) $s = 138$

Question 53

The following table shows the approximate number of males of Hispanic origin employed in the U.S. in 2005, broken down by age group. In what age interval does the empirical rule predict that 68 percent of all male Hispanic workers will fall Please round answers to the nearest year. $$\begin{array} { | c | c | c | c | } \hline \text { Age } & 15 - 24.9 & 25 - 54.9 & 55 - 64.9 \\\hline \begin{array} { c } \text { Employment } \\\text { (thousands) }\end{array} & 16,000 & 13,000 & 1,600 \\\hline\end{array}$$

A)31 - 42
B) 19 - 31
C) 19 - 42
D) 12 - 31
E) 12 - 42

Question 54

Calculate the standard deviation of X for the probability distribution. ​
Round your answer to two decimal places.
​ __________

Question 55

Compute the (sample) standard deviation for the data. Please round your answer to two decimal places. $2.8 , - 5.6,4.4,4.3 , - 0.2 , - 0.2$

A) $s = 7.21$
B) $s = 0.96$
C) $s = 3.8$
D) $s = 0.92$
E) $s = 14.42$

Question 56

Calculate the standard deviation of the given random variable X. Please, round your answer to two decimal places, if necessary.
X is the number of heads that come up when a coin is tossed three times.

A) $\sigma = 1.4$
B) $\sigma = 0.87$
C) $\sigma = 0.75$
D) $\sigma = 0.25$
E) $\sigma = 0.13$

Question 57

If we model after-tax household income by a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is bell-shaped and symmetric. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Country } & \text { U.S. } & \text { Canada } & \text { Switzerland } & \text { Germany } & \text { Sweden } \\\hline \begin{array} { c } \text { Mean Household } \\\text { Income }\end{array} & \$ 38,000 & \$ 35,000 & \$ 39,000 & \$ 34,000 & \$ 32,000 \\\hline \text { Standard Deviation } & \$ 21,000 & \$ 17,000 & \$ 16,000 & \$ 14,000 & \$ 11,000 \\\hline\end{array}$$ If we define a "poor" household as one whose after-tax income is at least 1.3 standard deviations below the mean, find the household income of a poor family in Switzerland.

A)$59,800 or less
B) $59,800 or more
C) $18,200 or less
D) $16,000 or less
E) $18,200 or more

Question 58

Calculate the standard deviation of X for the probability distribution. $$\begin{array} { | c | c | c | c | c | c | c | } \hline x & - 20 & - 13 & 1 & 13 & 20 & 25 \\\hline P ( X = x ) & 0.1 & 0.1 & 0.1 & 0.2 & 0 & 0.5 \\\hline\end{array}$$ Round your answer to two decimal places if necessary.

A)261.69
B) 162.19
C) 1,757.64
D) 11.9
E) 16.18

Question 59

Calculate the standard deviation of the given random variable X. Please round your answer to two decimal places.
Forty-five darts are thrown at a dartboard. The probability of hitting a bull's-eye is 0.4. Let X be the number of bull's-eyes hit.

A) $\sigma = 10.8$
B) $\sigma = 18$
C) $\sigma = 4.24$
D) $\sigma = 3.29$
E) $\sigma = 5.4$

Question 60

If we model after-tax household income by a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is bell-shaped and symmetric. Find the percent of canadian families which earned an after-tax income of $69,000 or more. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Country } & \text { U.S. } & \text { Canada } & \text { Switzerland } & \text { Germany } & \text { Sweden } \\\hline \begin{array} { c } \text { Mean Household } \\\text { Income }\end{array} & \$ 38,000 & \$ 35,000 & \$ 39,000 & \$ 34,000 & \$ 32,000 \\\hline \text { Standard Deviation } & \$ 21,000 & \$ 17,000 & \$ 16,000 & \$ 14,000 & \$ 11,000 \\\hline\end{array}$$

A)5%
B) 95%
C) 47.5%
D) 2.5%
E) 99.7%

Question 61

Find the expected value of a random variable X having the following probability distribution: $$\begin{array} { c c c c c } x & 10 & 20 & 30 & 40 \\P ( X = x ) & \frac { 20 } { 50 } & \frac { 10 } { 50 } & \frac { 15 } { 50 } & \frac { 5 } { 50 }\end{array}$$ Round your answer to tenth if necessary.

A) $E ( X ) = 21$
B) $E ( X ) = 16$
C) $E ( X ) = 25$
D) $E ( X ) = 12.5$
E) $E ( X ) = 10$

Question 62

Compute the (sample) standard deviation of the data sample. Round your answer to the nearest whole number, if necessary.
​ ​ __________

Question 63

Compute the (sample) variance and the standard deviation for the data.
​ ​
Please round your answers to two decimal places, if necessary.
​ __________
​ __________

Question 64

If we model after-tax household income by a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is bell-shaped and symmetric. If we define a "rich" household as one whose after-tax income is at least 1.3 standard deviations above the mean, find the household income of a rich family in Germany. ​
The household income of a rich family in Germany is __________ or __________ (more or less).

Question 65

Calculate the expected value, the variance, and the standard deviation of the given random variable X.
​
Forty-five darts are thrown at a dartboard. The probability of hitting a bull's-eye is 0.3. Let X be the number of bull's-eyes hit.
​
Please round your answers to two decimal places, if necessary.
​ __________
​ __________
​ __________

Question 66

Find the expected value of a random variable X having the following probability distribution: $$\begin{array} { c c c c c } x & 2 & 4 & 6 & 8 \\P ( X = x ) & \frac { 9 } { 40 } & \frac { 6 } { 40 } & \frac { 1 } { 40 } & \frac { 24 } { 40 }\end{array}$$ Round your answer to tenth if necessary.

A) $E ( X ) = 4$
B) $E ( X ) = 5$
C) $E ( X ) = 6$
D) $E ( X ) = 10$
E) $E ( X ) = 20$

Question 67

Calculate the expected value of X for the given probability distribution. $$\begin{array} { c c c c c } x & 1 & 2 & 3 & 4 \\P ( X = x ) & 0.6 & 0.1 & 0.1 & 0.2\end{array}$$

A) $E ( X ) = 1.6$
B) $E ( X ) = 2.1$
C) $E ( X ) = 2.4$
D) $E ( X ) = 1.9$
E) $E ( X ) = 2.3$

Question 68

The following is a sample of the percentage increases in the price of a house in eight regions of the U.S.
​
75, 125, 150, 150, 150, 215, 215, 300
​
Compute the mean of the given sample. Round answer to the nearest whole number.
​ __________
​
Compute the standard deviation of the given sample. Use the rounded value for the mean in your calculations. Round answer to the nearest whole number.
​ __________
​
Assuming the distribution of percentage housing price increases for all regions is symmetric and bell-shaped, 68 percent of all regions in the U.S. reported housing increases between __________ and __________. Please, use the rounded value for the standard deviation here.
​
Find the percentage of scores in the sample that fall in this range. Please round your answer to the nearest whole number.
​
__________%

Question 69

Find the median of 7, 4, 5, 6, 13, 7, 23, and 3. ​

A)6.5
B) 8.7
C) 13
D) 6
E) 10

Question 70

The following table shows the approximate number of males of Hispanic origin employed in the U.S., broken down by age group. $$\begin{array} { | c | c | c | c | } \hline \text { Age } & 15 - 24.9 & 25 - 54.9 & 55 - 64.9 \\\hline \begin{array} { c } \text { Employment } \\\text { (thousands) }\end{array} & 17,000 & 13,000 & 1,500 \\\hline\end{array}$$
Use the rounded midpoints of the given measurement classes to compute the expected value and the standard deviation of the age X of a male Hispanic worker in the U.S. Please round your answers to two decimal places. $\mu =$ __________ $\sigma =$ __________
In what age interval does the empirical rule predict that 68 percent of all male Hispanic workers will fall Please round answers to the nearest year.
from __________ to __________

Question 71

Calculate the expected value, the variance, and the standard deviation of the given random variable X. Please round your answers to two decimal places, if necessary.
​
​X is the number of tails that come up when a coin is tossed two times.
​ __________
​ __________
​ __________

Question 72

Calculate the standard deviation of X for the probability distribution. Round your answer to two decimal places if necessary. ​ __________

Question 73

Your company, Sonic Video, Inc., has conducted research that shows the following probability distribution, where X is the number of video arcades in a randomly chosen city with more than 500,000 inhabitants. ​
Compute the mean. Please round your answer to one decimal place. __________
Compute the variance. Use the rounded value for the mean in your calculations. Round your answer to one decimal place. __________
Compute the standard deviation. Use the rounded value for the variance in your calculations. Round your answer to one decimal place. __________
As CEO of Startrooper Video Unlimited, you wish to install a chain of video arcades in Sleepy City, U.S.A. The city council regulations require that the number of arcades be within the range shared by at least 75 percent of all cities. Find this range. Please round your answers to one decimal place.
from __________ to __________
Find the largest number of video arcades you should install so as to comply with this regulation.
The largest number is __________.

Question 74

If we model after-tax household income by a normal distribution, then the figures of a 1995 study imply the information in the following table. Assume that the distribution of incomes in each country is bell-shaped and symmetric. Find the percentage of swiss families which earned an after-tax income of $71,000 or more. Round your answer to one decimal place if necessary. ​
The percentage is __________%.

Question 75

Find the expected value of the following probability distribution. $$\begin{array} { c c c c c } x & 3 & 9 & 12 & 16 \\P ( X = x ) & 0.3 & 0.5 & 0.1 & 0.1\end{array}$$

A)7.3
B) 4
C) 2.5
D) 8.2
E) 10

Question 76

In your bid to be elected class representative, you have your election committee survey five randomly chosen students in your class and ask them to rank you on a scale of 0 - 10. Your rankings are 6, 2, 7, 4, 8.

(a) Find the sample mean, rounded to two decimal places.
$\bar { x } =$ __________

(b) Calculate the sample standard deviation, rounded to two decimal places.
$5 \approx$ __________

(c) Assuming the sample mean and standard deviation are indicative of the class as a whole, in what range does the empirical rule predict that approximately 68% of the class will rank you

Question 77

Compute the (sample) variance and the standard deviation for the data.
​ ​
Please round your answers to two decimal places.
​ __________
​ __________

Question 78

The following is a sample of tow ratings (in pounds) for some popular 2000 model light trucks:
​
2,000, 2,000, 4,000, 5,000, 6,000, 7,000, 7,000, 7,000, 8,000, 8,000
​
Compute the mean of the given sample. Round your answer to the nearest whole number.
​ __________
​
Compute the standard deviation of the given sample. Round your answer to the nearest whole number.
​ __________
​
Assuming the distribution of tow ratings for all popular light trucks is symmetric and bell-shaped, 68 percent of all light trucks have tow ratings between __________ and __________. Please, use the rounded value for the standard deviation here.
​
Find the percentage of scores in the sample that fall in this range.
​
__________%

Question 79

Calculate the standard deviation of X for the probability distribution. Round your answer to the whole number. ​ __________

Question 80

In 2000, 30 percent of all teenagers in some country had checking accounts. Your bank, TeenChex Inc., is interested in targeting teenagers who do not already have a checking account.
​
TeenChex selects a random sample of 1,000 teenagers. Find the number of teenagers without checking accounts it can expect.
​ __________
​
Find the standard deviation of this number. Please, round your answer to one decimal place.
​ __________
​
Fill in the missing quantities. Please round answers to the nearest whole number.
​
There is an approximately 95 percent chance that between __________ and __________ teenagers in the sample will not have checking accounts.