Question 1

The number of children in a family can be modelled using a continuous random variable.

Accepted Answer

A) True 
 B)False

Question 2

Suppose that $x$ has an exponential distribution with $\theta = 5$. Find $P ( x \leq 10 )$.

Accepted Answer

A)  $0.864665$ 
B)  $0.393469$ 
C)  $0.135335$ 
D)  $0.606531$ 
A)  $0.864665$ 
B)  $0.393469$ 
C)  $0.135335$ 
D)  $0.606531$

Question 3

A certain baseball player hits a home run in 7% of his at-bats. Consider his at-bats as independent events. Find the probability that this baseball player hits more than 42 home runs in 800 at-bats?

Accepted Answer

A) 0.93 
B) 0.9693 
C) 0.0307 
D) 0.07 
A) 0.93 
B) 0.9693 
C) 0.0307 
D) 0.07

Question 4

Suppose that $x$ has an exponential distribution with $\theta = 2.5$. Find $P ( x \geq 4 )$.

Accepted Answer

A)  $0.535261$ 
B)  $0.798103$ 
C)  $0.464739$ 
D)  $0.201897$ 
A)  $0.535261$ 
B)  $0.798103$ 
C)  $0.464739$ 
D)  $0.201897$

Question 5

Which one of the following suggests that the data set is approximately normal?

Accepted Answer

A)  A data set with $Q _ { 1 } = 1330 , Q _ { 3 } = 2940$, and $s = 2440$. 
B)  A data set with $Q _ { 1 } = 105 , Q _ { 3 } = 270$, and $s = 33$. 
C)  A data set with $Q _ { 1 } = 2.2 , Q _ { 3 } = 7.3$, and $s = 2.1$. 
D)  A data set with $Q _ { 1 } = 14 , Q _ { 3 } = 68$, and $s = 41$. 
A)  A data set with $Q _ { 1 } = 1330 , Q _ { 3 } = 2940$, and $s = 2440$. 
B)  A data set with $Q _ { 1 } = 105 , Q _ { 3 } = 270$, and $s = 33$. 
C)  A data set with $Q _ { 1 } = 2.2 , Q _ { 3 } = 7.3$, and $s = 2.1$. 
D)  A data set with $Q _ { 1 } = 14 , Q _ { 3 } = 68$, and $s = 41$.

Question 6

Use the standard normal distribution to find $$P ( - 2.50 < z < 1.50 ) .$$

Accepted Answer

A) .9270 
B) .8822 
C) .5496 
D) .6167 
A) .9270 
B) .8822 
C) .5496 
D) .6167

Question 7

An online retailer reimburses a customerʹs shipping charges if the customer does not
receive his order within one week. Delivery time (in days)is exponentially distributed
with a mean of 3.2 days. What percentage of customers have their shipping charges
reimbursed?

Accepted Answer

The answer of An online retailer reimburses a customerʹs shipping...

Question 8

Suppose that 88% of the stocks listed on a particular exchange increased in value
yesterday. Let x be the number of stocks that increased in value yesterday in a random of
72 stocks listed on the exchange. Find the mean and standard deviation of x.

Accepted Answer

Mean = μ = .88(72)=

Question 9

The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. Find the price for which 12.3% of milk vendors exceeded.

Accepted Answer

A) $3.238 
B) $3.316 
C) $3.084 
D) $3.215 
A) $3.238 
B) $3.316 
C) $3.084 
D) $3.215

Question 10

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 6.5 to 8.5 millimeters. Any ball bearing with a diameter of
Over 8.25 millimeters or under 6.75 millimeters is considered defective. What is the probability that
A randomly selected ball bearing is defective?

Accepted Answer

A) .75 
B) .25 
C) .50 
D) 0 
A) .75 
B) .25 
C) .50 
D) 0

Question 11

Suppose x is a random variable best described by a uniform probability distribution with c = 2 and d = 6. Find the value of a that makes the following probability statement true: $\mathrm { P } ( 2.5 \leq x \leq a ) = 0.5$

Accepted Answer

A) 3 
B) 0.8 
C) 4 
D) 4.5 
A) 3 
B) 0.8 
C) 4 
D) 4.5

Question 12

A certain baseball player hits a home run in 7% of his at-bats. Consider his at-bats as independent events. Find the probability that this baseball player hits at most 42 home runs in 800 at-bats?

Accepted Answer

A) 0.07 
B) 0.0307 
C) 0.9693 
D) 0.93 
A) 0.07 
B) 0.0307 
C) 0.9693 
D) 0.93

Question 13

Determine if it is appropriate to use the normal distribution to approximate a binomial
distribution when n = 41 and p = 0.6.

Accepted Answer

can use no

Question 14

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 78°F to 108°F. Find the temperature which is exceeded by the high temperatures on 90% of
The days in August.

Accepted Answer

A) 108°F 
B) 105°F 
C) 88°F 
D) 81°F 
A) 108°F 
B) 105°F 
C) 88°F 
D) 81°F

Question 15

Suppose x is a random variable best described by a uniform probability distribution with c = 30 and $d = 110 . \text { Find } P ( x > 94 )$

Accepted Answer

A) 0.2 
B) 0.02 
C) 0.16 
D) 0.8 
A) 0.2 
B) 0.02 
C) 0.16 
D) 0.8

Question 16

Which of the following is not a method used for determining whether data are from an approximately normal distribution?

Accepted Answer

A)  Compute the intervals $\bar { x } \pm s , \bar { x } \pm 2 s$, and $\bar { x } \pm 3 s$. The percentages of measurements falling in each should be approximately $68 \% , 95 \%$, and $100 \%$ respectively. 
B)  Find the interquartile range, IQR, and standard deviation, s, for the sample. Then $\frac { \mathrm { IQR } } { s } \approx 1.3$. 
C)  Construct a normal probability plot. The points should fall approximately on a straight line. 
D)  Construct a histogram or stem-and-leaf display. The shape of the graph or display should be uniform (evenly distributed). 
A)  Compute the intervals $\bar { x } \pm s , \bar { x } \pm 2 s$, and $\bar { x } \pm 3 s$. The percentages of measurements falling in each should be approximately $68 \% , 95 \%$, and $100 \%$ respectively. 
B)  Find the interquartile range, IQR, and standard deviation, s, for the sample. Then $\frac { \mathrm { IQR } } { s } \approx 1.3$. 
C)  Construct a normal probability plot. The points should fall approximately on a straight line. 
D)  Construct a histogram or stem-and-leaf display. The shape of the graph or display should be uniform (evenly distributed).

Question 17

A machine is set to pump cleanser into a process at the rate of 8 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the
Uniform distribution over the interval 7.5 to 9.5 gallons per minute. Find the variance of the
Distribution.

Accepted Answer

A) 5.33 
B) 0.08 
C) 0.33 
D) 24.08 
A) 5.33 
B) 0.08 
C) 0.33 
D) 24.08

Question 18

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 3$. Find the $z$-score that corresponds to the value $x = 72$.

Accepted Answer

A)  4 
B)  5 
C)  12 
D)  3 
A)  4 
B)  5 
C)  12 
D)  3

Question 19

Assume that x is a binomial random variable with n = 1000 and p = 0.80. Use a normal approximation to find $\mathrm { P } ( 800 < \mathrm { x } \leq 830 )$

Accepted Answer

A) 0.4920 
B) 0.4741 
C) 0.0753 
D) 0.4760 
A) 0.4920 
B) 0.4741 
C) 0.0753 
D) 0.4760

Question 20

The board of examiners that administers the real estate brokerʹs examination in a certain
state found that the mean score on the test was 588 and the standard deviation was 72. If
the board wants to set the passing score so that only the best 80% of all applicants pass,
what is the passing score? Assume that the scores are normally distributed.

Accepted Answer

Let @#LAT-DLM& be a score on this exam.

The number of children in a family can be modelled using a continuous random variable.

Suppose that $x$ has an exponential distribution with $\theta = 5$ . Find $P ( x \leq 10 )$ .

A certain baseball player hits a home run in 7% of his at-bats. Consider his at-bats as independent events. Find the probability that this baseball player hits more than 42 home runs in 800 at-bats?

Suppose that $x$ has an exponential distribution with $\theta = 2.5$ . Find $P ( x \geq 4 )$ .

Which one of the following suggests that the data set is approximately normal?

Use the standard normal distribution to find $P ( - 2.50 < z < 1.50 ) .$

An online retailer reimburses a customerʹs shipping charges if the customer does not receive his order within one week. Delivery time (in days)is exponentially distributed with a mean of 3.2 days. What percentage of customers have their shipping charges reimbursed?

Suppose that 88% of the stocks listed on a particular exchange increased in value yesterday. Let x be the number of stocks that increased in value yesterday in a random of 72 stocks listed on the exchange. Find the mean and standard deviation of x.

The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. Find the price for which 12.3% of milk vendors exceeded.

Suppose x is a random variable best described by a uniform probability distribution with c = 2 and d = 6. Find the value of a that makes the following probability statement true: $\mathrm { P } ( 2.5 \leq x \leq a ) = 0.5$

A certain baseball player hits a home run in 7% of his at-bats. Consider his at-bats as independent events. Find the probability that this baseball player hits at most 42 home runs in 800 at-bats?

Determine if it is appropriate to use the normal distribution to approximate a binomial distribution when n = 41 and p = 0.6.

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 78°F to 108°F. Find the temperature which is exceeded by the high temperatures on 90% of The days in August.

Suppose x is a random variable best described by a uniform probability distribution with c = 30 and $d = 110 . \text { Find } P ( x > 94 )$

Which of the following is not a method used for determining whether data are from an approximately normal distribution?

A machine is set to pump cleanser into a process at the rate of 8 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the Uniform distribution over the interval 7.5 to 9.5 gallons per minute. Find the variance of the Distribution.

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 3$ . Find the $z$ -score that corresponds to the value $x = 72$ .

Assume that x is a binomial random variable with n = 1000 and p = 0.80. Use a normal approximation to find $\mathrm { P } ( 800 < \mathrm { x } \leq 830 )$

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Discrete Random Variables

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Analysis of Variance: Comparing More Than Two Means

Simple Linear Regression

Multiple Regression and Model Building

Categorical Data Analysis

Nonparametric Statistics Available Online

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Exam 5: Continuous Random Variables

The number of children in a family can be modelled using a continuous random variable.

Suppose that xxx has an exponential distribution with θ=5\theta = 5θ=5 . Find P(x≤10)P ( x \leq 10 )P(x≤10) .

A certain baseball player hits a home run in 7% of his at-bats. Consider his at-bats as independent events. Find the probability that this baseball player hits more than 42 home runs in 800 at-bats?

Suppose that xxx has an exponential distribution with θ=2.5\theta = 2.5θ=2.5 . Find P(x≥4)P ( x \geq 4 )P(x≥4) .

Which one of the following suggests that the data set is approximately normal?

Use the standard normal distribution to find P(−2.50<z<1.50).P ( - 2.50 < z < 1.50 ) .P(−2.50<z<1.50).

An online retailer reimburses a customerʹs shipping charges if the customer does not receive his order within one week. Delivery time (in days)is exponentially distributed with a mean of 3.2 days. What percentage of customers have their shipping charges reimbursed?

Suppose that 88% of the stocks listed on a particular exchange increased in value yesterday. Let x be the number of stocks that increased in value yesterday in a random of 72 stocks listed on the exchange. Find the mean and standard deviation of x.

The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. Find the price for which 12.3% of milk vendors exceeded.

Suppose x is a random variable best described by a uniform probability distribution with c = 2 and d = 6. Find the value of a that makes the following probability statement true: P(2.5≤x≤a)=0.5\mathrm { P } ( 2.5 \leq x \leq a ) = 0.5P(2.5≤x≤a)=0.5

A certain baseball player hits a home run in 7% of his at-bats. Consider his at-bats as independent events. Find the probability that this baseball player hits at most 42 home runs in 800 at-bats?

Determine if it is appropriate to use the normal distribution to approximate a binomial distribution when n = 41 and p = 0.6.

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 78°F to 108°F. Find the temperature which is exceeded by the high temperatures on 90% of The days in August.

Suppose x is a random variable best described by a uniform probability distribution with c = 30 and d=110. Find P(x>94)d = 110 . \text { Find } P ( x > 94 )d=110. Find P(x>94)

Which of the following is not a method used for determining whether data are from an approximately normal distribution?

A machine is set to pump cleanser into a process at the rate of 8 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the Uniform distribution over the interval 7.5 to 9.5 gallons per minute. Find the variance of the Distribution.

Suppose a random variable xxx is best described by a normal distribution with μ=60\mu = 60μ=60 and σ=3\sigma = 3σ=3 . Find the zzz -score that corresponds to the value x=72x = 72x=72 .

Assume that x is a binomial random variable with n = 1000 and p = 0.80. Use a normal approximation to find P(800<x≤830)\mathrm { P } ( 800 < \mathrm { x } \leq 830 )P(800<x≤830)

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Discrete Random Variables

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Analysis of Variance: Comparing More Than Two Means

Simple Linear Regression

Multiple Regression and Model Building

Categorical Data Analysis

Nonparametric Statistics Available Online

Filters

Suppose that $x$ has an exponential distribution with $\theta = 5$ . Find $P ( x \leq 10 )$ .

Suppose that $x$ has an exponential distribution with $\theta = 2.5$ . Find $P ( x \geq 4 )$ .

Use the standard normal distribution to find $P ( - 2.50 < z < 1.50 ) .$

Suppose x is a random variable best described by a uniform probability distribution with c = 2 and d = 6. Find the value of a that makes the following probability statement true: $\mathrm { P } ( 2.5 \leq x \leq a ) = 0.5$

Suppose x is a random variable best described by a uniform probability distribution with c = 30 and $d = 110 . \text { Find } P ( x > 94 )$

Suppose a random variable $x$ is best described by a normal distribution with $\mu = 60$ and $\sigma = 3$ . Find the $z$ -score that corresponds to the value $x = 72$ .

Assume that x is a binomial random variable with n = 1000 and p = 0.80. Use a normal approximation to find $\mathrm { P } ( 800 < \mathrm { x } \leq 830 )$