Question 1

A student takes a true-false test that has 14 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(5)

Accepted Answer

A)  0.1222 
B)  0.0001 
C)  0.1833 
D)  0.0611 
A)  0.1222 
B)  0.0001 
C)  0.1833 
D)  0.0611

Question 2

There are 4,000 undergraduates registered at a certain college. Of them, 364 are taking one course, 496 are taking two courses, 460 are taking three courses, 1,512 are taking four courses, 1,056 are
Taking five courses, and 112 are taking six courses. Let X be the number of courses taken by a
Student randomly sampled from this population. Find the probability distribution of X.

Accepted Answer

A) $\begin{array} { c | c | c | c | c | c | c } 
x & 1 & 2 & 3 & 4 & 5 & 6 \
\hline P ( x ) & 0.1120 & 1.0560 & 1.5120 & 0.4600 & 0.4960 & 0.3640
\end{array}$ 
B) $\begin{array} { c | c | c | c | c | c | c } 
x & 1 & 2 & 3 & 4 & 5 & 6 \
\hline P ( x ) & 0.3640 & 0.4960 & 0.4600 & 1.5120 & 1.0560 & 0.1120
\end{array}$ 
C) $\begin{array} { c | c | c | c | c | c | c } 
x & 1 & 2 & 3 & 4 & 5 & 6 \
\hline P ( x ) & 0.0280 & 0.2640 & 0.3780 & 0.1150 & 0.1240 & 0.0910
\end{array}$ 
D)  $\begin{array} { c | c | c | c | c | c | c } 
x & 1 & 2 & 3 & 4 & 5 & 6 \
\hline P ( x ) & 0.0910 & 0.1240 & 0.1150 & 0.3780 & 0.2640 & 0.0280
\end{array}$ 
A) $\begin{array} { c | c | c | c | c | c | c } 
x & 1 & 2 & 3 & 4 & 5 & 6 \
\hline P ( x ) & 0.1120 & 1.0560 & 1.5120 & 0.4600 & 0.4960 & 0.3640
\end{array}$ 
B) $\begin{array} { c | c | c | c | c | c | c } 
x & 1 & 2 & 3 & 4 & 5 & 6 \
\hline P ( x ) & 0.3640 & 0.4960 & 0.4600 & 1.5120 & 1.0560 & 0.1120
\end{array}$ 
C) $\begin{array} { c | c | c | c | c | c | c } 
x & 1 & 2 & 3 & 4 & 5 & 6 \
\hline P ( x ) & 0.0280 & 0.2640 & 0.3780 & 0.1150 & 0.1240 & 0.0910
\end{array}$ 
D)  $\begin{array} { c | c | c | c | c | c | c } 
x & 1 & 2 & 3 & 4 & 5 & 6 \
\hline P ( x ) & 0.0910 & 0.1240 & 0.1150 & 0.3780 & 0.2640 & 0.0280
\end{array}$

Question 3

Determine the indicated probability for a Poisson random variable with the given values of $\lambda \text { and } t$ $\lambda = 0.8 , t = 5 , P ( \text { More than } 3 )$

Accepted Answer

A)  0.4335 
B)  0.4152 
C)  0.5665 
D)  0.2381 
A)  0.4335 
B)  0.4152 
C)  0.5665 
D)  0.2381

Question 4

In the game of craps, two dice are rolled, and people bet on the outcome. For example, you can bet $1 that the dice will total 11. The probability that you win is $\frac { 1 } { 18 }$ , and if you win, your profit is $15.
If you lose, you lose $1. What is the expected value of your profit?

Accepted Answer

A)  $0.83 
B)  -$0.94 
C)  -$0.11 
D)  $0.11 
A)  $0.83 
B)  -$0.94 
C)  -$0.11 
D)  $0.11

Question 5

The number of typographical errors in a document follows a Poisson distribution with a mean of 2 errors per page. Let X represent the number of errors on 4 pages. Find P(Greater than 1).

Accepted Answer

A)  0.5940 
B)  0.9862 
C)  0.9970 
D)  0.9997 
A)  0.5940 
B)  0.9862 
C)  0.9970 
D)  0.9997

Question 6

An environmental scientist obtains a sample of water from an irrigation canal that contains a certain type of bacteria at a concentration of 6 per milliliter. Find the mean number of bacteria in a 8-milliliter sample.

Accepted Answer

A)  2.4 
B)  48 
C)  6.9 
D)  6 
A)  2.4 
B)  48 
C)  6.9 
D)  6

Question 7

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p.
N =8, p = 0.6, P(3 or fewer)

Accepted Answer

A)  0.8263 
B)  0.0498 
C)  0.1737 
D)  0.4059 
A)  0.8263 
B)  0.0498 
C)  0.1737 
D)  0.4059

Question 8

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 12 adult dogs is studied.
What is the probability that more than 9 of them weigh 65 lb or more?

Accepted Answer

A)  0.0079 
B)  0.9644 
C)  0.0356 
D)  0.0011 
A)  0.0079 
B)  0.9644 
C)  0.0356 
D)  0.0011

Question 9

Determine the indicated probability for a Poisson random variable with the given values of $\lambda \text { and } t \text {. }$ $\lambda = 0.9 , t = 3 , P ( \text { Less than } 3 )$

Accepted Answer

A)  0.6469 
B)  0.7141 
C)  0.4936 
D)  0.5064 
A)  0.6469 
B)  0.7141 
C)  0.4936 
D)  0.5064

Question 10

The number of customers in a line at a supermarket express checkout counter is a random variable with the following probability distribution.

$\begin{array} { c | c | c | c | c | c | c } 
\boldsymbol { x } & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \boldsymbol { P } ( \boldsymbol { x } ) & 0.09 & 0.26 & 0.29 & 0.20 & 0.09 & 0.07
\end{array}$

Find P(2 or fewer).

Accepted Answer

A)  0.65 
B)  0.29 
C)  0.35 
D)  0.64 
A)  0.65 
B)  0.29 
C)  0.35 
D)  0.64

Question 11

Ten students are chosen from a statistics class of 22 students. Let X be the number who got an "A" in the class. Is this a binomial distribution, and if so, what is the number of trials?

Accepted Answer

A)  Not binomial 
B)  Binomial, n = 10 
C)  Binomial, n = 12 
D)  Binomial, n = 22 
A)  Not binomial 
B)  Binomial, n = 10 
C)  Binomial, n = 12 
D)  Binomial, n = 22

Question 12

Determine whether the random variable described is discrete or continuous. The number of minutes you must wait in line at the grocery store

Accepted Answer

A)  continuous 
B)  discrete 
A)  continuous 
B)  discrete

Question 13

In a poll conducted by a survey firm, 76% of respondents said that their jobs were sometimes or always stressful. Eight workers are chosen at random. What is the standard deviation of the Number of workers who find their jobs stressful?

Accepted Answer

A)  1.21 
B)  0.43 
C)  1.46 
D)  2.47 
A)  1.21 
B)  0.43 
C)  1.46 
D)  2.47

Question 14

In a poll conducted by a survey firm, 84% of respondents said that their jobs were sometimes or always stressful. Ten workers are chosen at random. What is the probability that exactly 6 of them Find their jobs stressful?

Accepted Answer

A)  0.0018 
B)  0.0483 
C)  0.9517 
D)  0.0012 
A)  0.0018 
B)  0.0483 
C)  0.9517 
D)  0.0012

Question 15

An investor is considering a $25,000 investment in a start-up company. She estimates that she has probability 0.2 of a $15,000 loss, probability 0.15 of a $20,000 loss, probability 0.05 of a $40,000 Profit, and probability 0.6 of breaking even (a profit of $0). What is the expected value of the profit?

Accepted Answer

A)  $11,000 
B)  $1,667 
C)  -$4,000 
D)  $8,000 
A)  $11,000 
B)  $1,667 
C)  -$4,000 
D)  $8,000

Question 16

A survey asked 808 people how many times per week they dine out at a restaurant. The results are presented in the following table.
 
$\begin{array} { c c } 
\hline \text { Number of Times } & \text { Frequency } \
\hline 0 & 116 \
1 & 230 \
2 & 222 \
3 & 110 \
4 & 69 \
5 & 25 \
6 & 30 \
7 & 608
\end{array}$
 
Consider the 808 people to be a population. Let X be the number of times per week a person dines out For a person sampled at random from this population. Find the probability that a person does not Dine out at all.

Accepted Answer

A)  0 
B)  0.144 
C)  0.285 
D)  0.428 
A)  0 
B)  0.144 
C)  0.285 
D)  0.428

A student takes a true-false test that has 14 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(5)

Determine the indicated probability for a Poisson random variable with the given values of $\lambda \text { and } t$ $\lambda = 0.8 , t = 5 , P ( \text { More than } 3 )$

In the game of craps, two dice are rolled, and people bet on the outcome. For example, you can bet $1 that the dice will total 11. The probability that you win is $\frac { 1 } { 18 }$ , and if you win, your profit is $15. If you lose, you lose $1. What is the expected value of your profit?

The number of typographical errors in a document follows a Poisson distribution with a mean of 2 errors per page. Let X represent the number of errors on 4 pages. Find P(Greater than 1).

An environmental scientist obtains a sample of water from an irrigation canal that contains a certain type of bacteria at a concentration of 6 per milliliter. Find the mean number of bacteria in a 8-milliliter sample.

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. N =8, p = 0.6, P(3 or fewer)

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 12 adult dogs is studied. What is the probability that more than 9 of them weigh 65 lb or more?

Determine the indicated probability for a Poisson random variable with the given values of $\lambda \text { and } t \text {. }$ $\lambda = 0.9 , t = 3 , P ( \text { Less than } 3 )$

The number of customers in a line at a supermarket express checkout counter is a random variable with the following probability distribution. 0 1 2 3 4 5 ( ) 0.09 0.26 0.29 0.20 0.09 0.07 Find P(2 or fewer).

Ten students are chosen from a statistics class of 22 students. Let X be the number who got an "A" in the class. Is this a binomial distribution, and if so, what is the number of trials?

Determine whether the random variable described is discrete or continuous. The number of minutes you must wait in line at the grocery store

In a poll conducted by a survey firm, 76% of respondents said that their jobs were sometimes or always stressful. Eight workers are chosen at random. What is the standard deviation of the Number of workers who find their jobs stressful?

In a poll conducted by a survey firm, 84% of respondents said that their jobs were sometimes or always stressful. Ten workers are chosen at random. What is the probability that exactly 6 of them Find their jobs stressful?

Basic Ideas

Graphical Summaries of Data

Numerical Summaries of Data

Summarizing Bivariate Data

Probability

The Normal Distribution

Confidence Intervals

Hypothesis Testing

Two-Sample Confidence Intervals

Two-Sample Hypothesis Tests

Tests With Qualitative Data

Inference in Linear Models

Analysis of Variance

Nonparametric Statistics

Filters

Exam 6: Discrete Probability Distributions

A student takes a true-false test that has 14 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(5)

Determine the indicated probability for a Poisson random variable with the given values of λ and t\lambda \text { and } tλ and t λ=0.8,t=5,P( More than 3)\lambda = 0.8 , t = 5 , P ( \text { More than } 3 )λ=0.8,t=5,P( More than 3)

In the game of craps, two dice are rolled, and people bet on the outcome. For example, you can bet $1 that the dice will total 11. The probability that you win is 118\frac { 1 } { 18 }181​ , and if you win, your profit is $15. If you lose, you lose $1. What is the expected value of your profit?

The number of typographical errors in a document follows a Poisson distribution with a mean of 2 errors per page. Let X represent the number of errors on 4 pages. Find P(Greater than 1).

An environmental scientist obtains a sample of water from an irrigation canal that contains a certain type of bacteria at a concentration of 6 per milliliter. Find the mean number of bacteria in a 8-milliliter sample.

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. N =8, p = 0.6, P(3 or fewer)

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 12 adult dogs is studied. What is the probability that more than 9 of them weigh 65 lb or more?

Determine the indicated probability for a Poisson random variable with the given values of λ and t. \lambda \text { and } t \text {. }λ and t. λ=0.9,t=3,P( Less than 3)\lambda = 0.9 , t = 3 , P ( \text { Less than } 3 )λ=0.9,t=3,P( Less than 3)

The number of customers in a line at a supermarket express checkout counter is a random variable with the following probability distribution. 0 1 2 3 4 5 ( ) 0.09 0.26 0.29 0.20 0.09 0.07 Find P(2 or fewer).

Ten students are chosen from a statistics class of 22 students. Let X be the number who got an "A" in the class. Is this a binomial distribution, and if so, what is the number of trials?

Determine whether the random variable described is discrete or continuous. The number of minutes you must wait in line at the grocery store

In a poll conducted by a survey firm, 76% of respondents said that their jobs were sometimes or always stressful. Eight workers are chosen at random. What is the standard deviation of the Number of workers who find their jobs stressful?

In a poll conducted by a survey firm, 84% of respondents said that their jobs were sometimes or always stressful. Ten workers are chosen at random. What is the probability that exactly 6 of them Find their jobs stressful?

Basic Ideas

Graphical Summaries of Data

Numerical Summaries of Data

Summarizing Bivariate Data

Probability

The Normal Distribution

Confidence Intervals

Hypothesis Testing

Two-Sample Confidence Intervals

Two-Sample Hypothesis Tests

Tests With Qualitative Data

Inference in Linear Models

Analysis of Variance

Nonparametric Statistics

Filters

Determine the indicated probability for a Poisson random variable with the given values of $\lambda \text { and } t$ $\lambda = 0.8 , t = 5 , P ( \text { More than } 3 )$

In the game of craps, two dice are rolled, and people bet on the outcome. For example, you can bet $1 that the dice will total 11. The probability that you win is $\frac { 1 } { 18 }$ , and if you win, your profit is $15. If you lose, you lose $1. What is the expected value of your profit?

Determine the indicated probability for a Poisson random variable with the given values of $\lambda \text { and } t \text {. }$ $\lambda = 0.9 , t = 3 , P ( \text { Less than } 3 )$