Question 1

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.) ?

Accepted Answer

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

Question 2

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.

Accepted Answer

0.3707

Question 3

Suppose X is a normal random variable with $\mu = 370$ and $\sigma = 60$ . Find the value, rounding to four decimal places, of
​ $P ( 430 \leq X \leq 460 ) =$ __________

Accepted Answer

0.0919

Question 4

X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X \leq 2 )$ . Round your answer to five decimal places.
​ $P ( X \leq 2 ) =$ __________

Accepted Answer

The answer of X is a binomial variable with \(n...

Question 5

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.
​

Accepted Answer

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 
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 6

12 darts are thrown at a dartboard. The probability of hitting a bull's-eye is 0.1. Let X be the number of bull's-eyes hit. Calculate the expected value of the given random variable X.

Accepted Answer

A)   $E ( X ) = 0.6$ 
B)  $E ( X ) = 1$ 
C)  $E ( X ) = 1.2$ 
D)  $E ( X ) = 6$ 
E)  $E ( X ) = 2$ 
A)   $E ( X ) = 0.6$ 
B)  $E ( X ) = 1$ 
C)  $E ( X ) = 1.2$ 
D)  $E ( X ) = 6$ 
E)  $E ( X ) = 2$

Question 7

X is a binomial variable with $n = 7$ and $p = 0.4$ . Compute $P ( 1 \leq X \leq 3 )$ . Round your answer to four decimal places.
​ $P ( 1 \leq X \leq 3 ) =$ __________

Accepted Answer

The answer of X is a binomial variable with \(n...

Question 8

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  ?

Accepted Answer

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

Question 9

X is the number of green marbles that Stej has in his hand after he selects 5 marbles from a bag containing 5 red marbles and 1 green ones and then notes how many there are of each color. Take each outcome to be a pair of numbers. (# of green marbles, # of red ones).  
List the values of X for all the outcomes.

Accepted Answer

A)   Outcome $( 0,5 ) ( 1,4 )$
Value of $X \quad 5 \quad 4$ 
B)    Outcome $( 0,5 ) ( 1,4 )$
Value of $X$ 
C)    Outcome $( 0,5 ) ( 1,4 )$
$\begin{array} { l l l } \text { Value of } X & 0 & 1 \end{array}$ 
D)    Outcome $( 0,5 ) ( 1,4 )$
Value of $X \quad 1 \quad 0$ 
E)    Outcome $( 0,5 ) ( 1,4 )$
Value of $X \quad 5 \quad 5$ 
A)   Outcome $( 0,5 ) ( 1,4 )$
Value of $X \quad 5 \quad 4$ 
B)    Outcome $( 0,5 ) ( 1,4 )$
Value of $X$ 
C)    Outcome $( 0,5 ) ( 1,4 )$
$\begin{array} { l l l } \text { Value of } X & 0 & 1 \end{array}$ 
D)    Outcome $( 0,5 ) ( 1,4 )$
Value of $X \quad 1 \quad 0$ 
E)    Outcome $( 0,5 ) ( 1,4 )$
Value of $X \quad 5 \quad 5$

Question 10

Let U be the higher number when two dice are rolled. Calculate the expected value of the given random variable U. Round your answer to three decimal places.
​ $E ( U ) =$ __________

Accepted Answer

The answer of Let U be the higher number when...

Question 11

The following table shows the distribution of household incomes for a sample of 1,000 households in the U.S. with incomes up to $100,000.

Use this information to estimate, to the nearest $1,000, the average household income for such households.
The average household income is __________.

Accepted Answer

The answer of The following table shows the distribution of...

Question 12

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. $$\begin{array} { | l | l | l | } 
\hline \text { Task } & \begin{array} { l } 
\text { Mean Time } \
\text { (minutes) }
\end{array} & \begin{array} { l } 
\text { Standard } \
\text { Deviation }
\end{array} \
\hline \text { Task 1: Descriptive Analysis of Data } & 12.5 & 6.0 \
\hline \text { Task 2: Standardizing Scores } & 11.9 & 9.0 \
\hline \text { Task 3: Poison Probability Table } & 7.3 & 3.9 \
\hline \text { Task 4:Areas Under Normal Curve } & 9.1 & 5.5 \
\hline
\end{array}$$

Accepted Answer

The answer of This exercise is based on the following...

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

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)    $P ( - 1.6 \leq Z \leq 0 ) = 0.5648$ 
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 15

Given the probability distribution below, calculate the expected value of X. $$\begin{array} { c c c c c c c } 
x & - 4 & - 2 & 0 & 3 & 7 & 16 \
P ( X = x ) & 0.1 & 0.2 & 0.3 & 0.2 & 0 & 0.2
\end{array}$$ ​ $$\mu = E ( X )$$ __________​

Accepted Answer

The answer of Given the probability distribution below, calculate the...

Question 16

According to a study, the probability that a randomly selected teenager watched a rented video at least once during a week was 0.76. What is the probability that at least 8 teenagers in a group of 10 watched a rented movie at least once last week  Round your answer to two decimal places.

Accepted Answer

The answer of According to a study, the probability that...

Question 17

The following table shows the distribution of household incomes for a sample of 1,000 households in the U.S. with incomes up to $100,000. $$\begin{array} { l | l | l | l | l | l | } 
\hline \text { Income Bracket } & 0 - 19,999 & 20,000 - 39,999 & 40,000 - 59,999 & 60,000 - 79,999 & 80,000 - 99,999 \
\hline \text { Households } & 270 & 290 & 200 & 140 & 100 \
\hline
\end{array}$$   Let X be the midpoint of a bracket in which a household falls.
Find the probability that a U.S. household has a value of X of more than 50,000.

Accepted Answer

A)  $P ( X > 50,000 ) = 0.27$ 
B)    $P ( X > 50,000 ) = 0.1$ 
C)    $P ( X > 50,000 ) = 0.44$ 
D)    $P ( X > 50,000 ) = 0.24$ 
E)    $P ( X > 50,000 ) = 0.29$ 
A)  $P ( X > 50,000 ) = 0.27$ 
B)    $P ( X > 50,000 ) = 0.1$ 
C)    $P ( X > 50,000 ) = 0.44$ 
D)    $P ( X > 50,000 ) = 0.24$ 
E)    $P ( X > 50,000 ) = 0.29$

Question 18

Calculate the expected value of X for the given probability distribution: $$\begin{array} { c c c c c c c } 
x & - 20 & - 10 & 0 & 10 & 20 & 30 \
P ( X = x ) & 0.1 & 0.2 & 0.3 & 0.1 & 0.1 & 0.2
\end{array}$$ ​ $$E ( X ) =$$ __________

Accepted Answer

The answer of Calculate the expected value of X for...

Question 19

According to a July, 1999, article in the New York Times, 13.5% of Internet stocks that entered the market in 1999 ended up trading below their initial offering prices. If you were an investor who purchased 3 Internet stocks at their initial offering prices, what was the probability that at least 2 of them would end up trading at or above their initial offering price  (Round your answer to four decimal places.)

Accepted Answer

The answer of According to a July, 1999, article in...

Question 20

The following table shows the approximate numbers of school goers in the U.S. (residents who attended some educational institution) in 1998, broken down by age group. Use the rounded midpoints of the given measurement classes to compute the probability distribution of the age  X of a school goer. (Round probabilities to two decimal places.) Hence compute the expected value of X. $$\begin{array} { c c c c c c c } 
\text { Age } & 3 - 6.9 & 7 - 12.9 & 13 - 16.9 & 17 - 22.9 & 23 - 26.9 & 27 - 42.9 \
\begin{array} { c } 
\text { Population } \
\text { (Millions) }
\end{array} & 11 & 22 & 16 & 15 & 4 & 7
\end{array}$$

Accepted Answer

A)  $E ( X ) = 15.2$ 
B)  $E ( X ) = 0.99$ 
C)  $E ( X ) = 7.65$ 
D)  $E ( X ) = 12.05$ 
E)  $E ( X ) = 10.8$ 
A)  $E ( X ) = 15.2$ 
B)  $E ( X ) = 0.99$ 
C)  $E ( X ) = 7.65$ 
D)  $E ( X ) = 12.05$ 
E)  $E ( X ) = 10.8$

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.) ?

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.

Suppose X is a normal random variable with $\mu = 370$ and $\sigma = 60$ . Find the value, rounding to four decimal places, of $P ( 430 \leq X \leq 460 ) =$ __________

X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X \leq 2 )$ . Round your answer to five decimal places. $P ( X \leq 2 ) =$ __________

12 darts are thrown at a dartboard. The probability of hitting a bull's-eye is 0.1. Let X be the number of bull's-eyes hit. Calculate the expected value of the given random variable X.

X is a binomial variable with $n = 7$ and $p = 0.4$ . Compute $P ( 1 \leq X \leq 3 )$ . Round your answer to four decimal places. $P ( 1 \leq X \leq 3 ) =$ __________

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 ?

Let U be the higher number when two dice are rolled. Calculate the expected value of the given random variable U. Round your answer to three decimal places. $E ( U ) =$ __________

The following table shows the distribution of household incomes for a sample of 1,000 households in the U.S. with incomes up to $100,000. Use this information to estimate, to the nearest $1,000, the average household income for such households. The average household income is __________.

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

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

Given the probability distribution below, calculate the expected value of X. x -4 -2 0 3 7 16 P(X=x) 0.1 0.2 0.3 0.2 0 0.2 $\mu = E ( X )$ __________

According to a study, the probability that a randomly selected teenager watched a rented video at least once during a week was 0.76. What is the probability that at least 8 teenagers in a group of 10 watched a rented movie at least once last week Round your answer to two decimal places.

Calculate the expected value of X for the given probability distribution: x -20 -10 0 10 20 30 P(X=x) 0.1 0.2 0.3 0.1 0.1 0.2 $E ( X ) =$ __________

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Matrix Algebra and Applications

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Introduction to the Derivative

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Exam 9: Random Variables and Statistics

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.) ?

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.

Suppose X is a normal random variable with μ=370\mu = 370μ=370 and σ=60\sigma = 60σ=60 . Find the value, rounding to four decimal places, of ​ P(430≤X≤460)=P ( 430 \leq X \leq 460 ) =P(430≤X≤460)= __________

X is a binomial variable with n=6n = 6n=6 and p=0.4p = 0.4p=0.4 . Compute P(X≤2)P ( X \leq 2 )P(X≤2) . Round your answer to five decimal places. ​ P(X≤2)=P ( X \leq 2 ) =P(X≤2)= __________

12 darts are thrown at a dartboard. The probability of hitting a bull's-eye is 0.1. Let X be the number of bull's-eyes hit. Calculate the expected value of the given random variable X.

X is a binomial variable with n=7n = 7n=7 and p=0.4p = 0.4p=0.4 . Compute P(1≤X≤3)P ( 1 \leq X \leq 3 )P(1≤X≤3) . Round your answer to four decimal places. ​ P(1≤X≤3)=P ( 1 \leq X \leq 3 ) =P(1≤X≤3)= __________

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 ?

Let U be the higher number when two dice are rolled. Calculate the expected value of the given random variable U. Round your answer to three decimal places. ​ E(U)=E ( U ) =E(U)= __________

The following table shows the distribution of household incomes for a sample of 1,000 households in the U.S. with incomes up to $100,000. Use this information to estimate, to the nearest $1,000, the average household income for such households. The average household income is __________.

Compute the (sample) standard deviation for the data. Please round your answer to two decimal places. 5,2,5,−4,0,165,2,5 , - 4,0,165,2,5,−4,0,16

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

Given the probability distribution below, calculate the expected value of X. x -4 -2 0 3 7 16 P(X=x) 0.1 0.2 0.3 0.2 0 0.2 ​ μ=E(X)\mu = E ( X )μ=E(X) __________​

According to a study, the probability that a randomly selected teenager watched a rented video at least once during a week was 0.76. What is the probability that at least 8 teenagers in a group of 10 watched a rented movie at least once last week Round your answer to two decimal places.

Calculate the expected value of X for the given probability distribution: x -20 -10 0 10 20 30 P(X=x) 0.1 0.2 0.3 0.1 0.1 0.2 ​ E(X)=E ( X ) =E(X)= __________

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Suppose X is a normal random variable with $\mu = 370$ and $\sigma = 60$ . Find the value, rounding to four decimal places, of $P ( 430 \leq X \leq 460 ) =$ __________

X is a binomial variable with $n = 6$ and $p = 0.4$ . Compute $P ( X \leq 2 )$ . Round your answer to five decimal places. $P ( X \leq 2 ) =$ __________

X is a binomial variable with $n = 7$ and $p = 0.4$ . Compute $P ( 1 \leq X \leq 3 )$ . Round your answer to four decimal places. $P ( 1 \leq X \leq 3 ) =$ __________

Let U be the higher number when two dice are rolled. Calculate the expected value of the given random variable U. Round your answer to three decimal places. $E ( U ) =$ __________

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

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

Given the probability distribution below, calculate the expected value of X. x -4 -2 0 3 7 16 P(X=x) 0.1 0.2 0.3 0.2 0 0.2 $\mu = E ( X )$ __________

Calculate the expected value of X for the given probability distribution: x -20 -10 0 10 20 30 P(X=x) 0.1 0.2 0.3 0.1 0.1 0.2 $E ( X ) =$ __________