Question 1

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p.
N = 15, p = 0.9, P(14)

Accepted Answer

A)  0.2288 
B)  0.0000 
C)  0.3432 
D)  0.9000 
A)  0.2288 
B)  0.0000 
C)  0.3432 
D)  0.9000

Question 2

An environmental scientist obtains a sample of water from an irrigation canal that contains a certain type of bacteria at a concentration of 2 per milliliter. Find the standard deviation of the number of Bacteria in a 4-milliliter sample.

Accepted Answer

A)  8 
B)  1.4 
C)  2.8 
D)  2 
A)  8 
B)  1.4 
C)  2.8 
D)  2

Question 3

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(5).

Accepted Answer

A)  0.1221 
B)  0.0916 
C)  0.9639 
D)  0.0361 
A)  0.1221 
B)  0.0916 
C)  0.9639 
D)  0.0361

Question 4

The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Compute the mean $\mu _ { x }$

$\begin{array} { c | c c c c c } 
x & 0 & 1 & 2 & 3 & 4 \
\hline P ( x ) & 0.06 & 0.66 & 0.16 & 0.09 & 0.03
\end{array}$

Accepted Answer

A)  1.37 
B)  0.71 
C)  1.43 
D)  0.84 
A)  1.37 
B)  0.71 
C)  1.43 
D)  0.84

Question 5

At an airport, 77% of recent flights have arrived on time. A sample of 11 flights is studied. What is the mean number of flights that are on time?

Accepted Answer

A)  1.95 
B)  8.47 
C)  2.53 
D)  2.91 
A)  1.95 
B)  8.47 
C)  2.53 
D)  2.91

Question 6

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p.
N = 15, p = 0.9, P(13 or more)

Accepted Answer

A)  0.9444 
B)  0.5490 
C)  0.1841 
D)  0.8159 
A)  0.9444 
B)  0.5490 
C)  0.1841 
D)  0.8159

Question 7

A die is rolled 11 times. Let X be the sum of the numbers obtained. Is this a binomial distribution, and if so, what is the number of trials?

Accepted Answer

A)  Not binomial 
B)  Binomial, n = 6 
C)  Binomial, n = 11 
A)  Not binomial 
B)  Binomial, n = 6 
C)  Binomial, n = 11

Question 8

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

$\begin{array}{l}
\begin{array} { c | c | c | c | c | c | c } 
\boldsymbol { x } & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \boldsymbol { P } ( \boldsymbol { x } ) & 0.11 & 0.22 & 0.31 & 0.16 & 0.09 & 0.11
\end{array}\\
\text { Compute the standard deviation } \sigma _ { x } \text {. }
\end{array}$

Accepted Answer

A)  2.12 
B)  2.23 
C)  4.48 
D)  1.46 
A)  2.12 
B)  2.23 
C)  4.48 
D)  1.46

Question 9

It is estimated that 45% of households own a riding lawn mower. A sample of 15 households is studied. What is the probability that exactly 7 of these own a riding lawn mower?

Accepted Answer

A)  0.8353 
B)  0.1647 
C)  0.7987 
D)  0.2013 
A)  0.8353 
B)  0.1647 
C)  0.7987 
D)  0.2013

Question 10

Determine whether the table represents a discrete probability distribution.
 $\begin{array} { c c } 
\hline x & P ( x ) \
\hline - 2 & 0.25 \
- 1 & 0.3 \
0 & 0.4 \
1 & 0.05 \
\hline
\end{array}$

Accepted Answer

A) True 
 B)False

Question 11

In a poll conducted by a survey firm, 73% of respondents said that their jobs were sometimes or always stressful. Eight workers are chosen at random. What is the mean number of workers who Find their job stressful?

Accepted Answer

A)  5.84 
B)  1.58 
C)  1.26 
D)  2.16 
A)  5.84 
B)  1.58 
C)  1.26 
D)  2.16

Question 12

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 16 adult dogs is studied.
What is the probability that no more than 3 of them weigh 65 lb or more?

Accepted Answer

A)  0.9719 
B)  0.9934 
C)  0.0066 
D)  0.0281 
A)  0.9719 
B)  0.9934 
C)  0.0066 
D)  0.0281

Question 13

The number of typographical errors in a document follows a Poisson distribution with a mean of 4 errors per page. Let X represent the number of errors on 2 pages. Find $\sigma _ { x }$

Accepted Answer

A)  3.8 
B)  2.8 
C)  8 
D)  4 
A)  3.8 
B)  2.8 
C)  8 
D)  4

Question 14

A survey asked 818 people how many times per week they dine out at a restaurant. The results are presented in the following table.

$\begin{array} { c c } 
\hline \text { Number of Times } & \text { Frequency } \
\hline 0 & 111 \
1 & 235 \
2 & 228 \
3 & 114 \
4 & 73 \
5 & 24 \
6 & 27 \
7 & 6 \
\hline \text { Total } & 818
\end{array}$
 
Consider the 818 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. Compute the mean

Accepted Answer

A)  1.5 
B)  2.2 
C)  2.3 
D)  2.0 
A)  1.5 
B)  2.2 
C)  2.3 
D)  2.0

Question 15

At an airport, 77% of recent flights have arrived on time. A sample of 11 flights is studied. Find the probability that no more than 4 of them were on time.

Accepted Answer

A)  0.0039 
B)  0.0046 
C)  0.9954 
D)  0.9961 
A)  0.0039 
B)  0.0046 
C)  0.9954 
D)  0.9961

Question 16

Last year, a manufacturer produced 1,950,000 DVD players. Of these, approximately 5% were defective. Assume that a simple random sample of n = 230 players is drawn. Use the Poisson Approximation to the binomial distribution to compute the probability that exactly nineteen of the 230 DVD players were defective.

Accepted Answer

A)  0.0119 
B)  0.0826 
C)  0.0068 
D)  0.0196 
A)  0.0119 
B)  0.0826 
C)  0.0068 
D)  0.0196

Question 17

An investor is considering a $25,000 investment in a start-up company. She estimates that she has probability 0.15 of a $20,000 loss, probability 0.1 of a $30,000 profit, probability 0.25 of a $40,000 Profit, and probability 0.5 of breaking even (a profit of $0). What is the expected value of the profit?

Accepted Answer

A)  $22,500 
B)  $10,000 
C)  $16,000 
D)  $16,667 
A)  $22,500 
B)  $10,000 
C)  $16,000 
D)  $16,667

Question 18

The number of typographical errors in a document follows a Poisson distribution with a mean of 4 errors per page. Let X represent the number of errors on 2 pages. Find $\mu _ { x ^ { * } }$

Accepted Answer

A)  4 
B)  9 
C)  8 
D)  2.8 
A)  4 
B)  9 
C)  8 
D)  2.8

Question 19

It is estimated that 35% of households own a riding lawn mower. A sample of 10 households is studied. What is the standard deviation of the number of households who own a riding lawn mower?

Accepted Answer

A)  3.5 
B)  1.5083 
C)  2.275 
D)  10 
A)  3.5 
B)  1.5083 
C)  2.275 
D)  10

Question 20

A coin is tossed until a head appears. Let X be the number of tosses. Is this a binomial distribution, and if so, what is the number of trials?

Accepted Answer

A)  Not binomial 
B)  Binomial, n = X 
C)  Binomial, n = 2 
A)  Not binomial 
B)  Binomial, n = X 
C)  Binomial, n = 2

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. N = 15, p = 0.9, P(14)

An environmental scientist obtains a sample of water from an irrigation canal that contains a certain type of bacteria at a concentration of 2 per milliliter. Find the standard deviation of the number of Bacteria in a 4-milliliter sample.

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(5).

The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Compute the mean $\mu _ { x }$ x 0 1 2 3 4 P(x) 0.06 0.66 0.16 0.09 0.03

At an airport, 77% of recent flights have arrived on time. A sample of 11 flights is studied. What is the mean number of flights that are on time?

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. N = 15, p = 0.9, P(13 or more)

A die is rolled 11 times. Let X be the sum of the numbers obtained. Is this a binomial distribution, and if so, what is the number of trials?

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 ( ) 0.11 0.22 0.31 0.16 0.09 0.11 Compute the standard deviation .

It is estimated that 45% of households own a riding lawn mower. A sample of 15 households is studied. What is the probability that exactly 7 of these own a riding lawn mower?

Determine whether the table represents a discrete probability distribution. x P(x) -2 0.25 -1 0.3 0 0.4 1 0.05

In a poll conducted by a survey firm, 73% of respondents said that their jobs were sometimes or always stressful. Eight workers are chosen at random. What is the mean number of workers who Find their job stressful?

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 16 adult dogs is studied. What is the probability that no more than 3 of them weigh 65 lb or more?

The number of typographical errors in a document follows a Poisson distribution with a mean of 4 errors per page. Let X represent the number of errors on 2 pages. Find $\sigma _ { x }$

At an airport, 77% of recent flights have arrived on time. A sample of 11 flights is studied. Find the probability that no more than 4 of them were on time.

The number of typographical errors in a document follows a Poisson distribution with a mean of 4 errors per page. Let X represent the number of errors on 2 pages. Find $\mu _ { x ^ { * } }$

It is estimated that 35% of households own a riding lawn mower. A sample of 10 households is studied. What is the standard deviation of the number of households who own a riding lawn mower?

A coin is tossed until a head appears. Let X be the number of tosses. Is this a binomial distribution, and if so, what is the number of trials?

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

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. N = 15, p = 0.9, P(14)

An environmental scientist obtains a sample of water from an irrigation canal that contains a certain type of bacteria at a concentration of 2 per milliliter. Find the standard deviation of the number of Bacteria in a 4-milliliter sample.

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(5).

The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Compute the mean μx\mu _ { x }μx​ x 0 1 2 3 4 P(x) 0.06 0.66 0.16 0.09 0.03

At an airport, 77% of recent flights have arrived on time. A sample of 11 flights is studied. What is the mean number of flights that are on time?

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. N = 15, p = 0.9, P(13 or more)

A die is rolled 11 times. Let X be the sum of the numbers obtained. Is this a binomial distribution, and if so, what is the number of trials?

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 ( ) 0.11 0.22 0.31 0.16 0.09 0.11 Compute the standard deviation .

It is estimated that 45% of households own a riding lawn mower. A sample of 15 households is studied. What is the probability that exactly 7 of these own a riding lawn mower?

Determine whether the table represents a discrete probability distribution. x P(x) -2 0.25 -1 0.3 0 0.4 1 0.05

In a poll conducted by a survey firm, 73% of respondents said that their jobs were sometimes or always stressful. Eight workers are chosen at random. What is the mean number of workers who Find their job stressful?

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 16 adult dogs is studied. What is the probability that no more than 3 of them weigh 65 lb or more?

The number of typographical errors in a document follows a Poisson distribution with a mean of 4 errors per page. Let X represent the number of errors on 2 pages. Find σx\sigma _ { x }σx​

At an airport, 77% of recent flights have arrived on time. A sample of 11 flights is studied. Find the probability that no more than 4 of them were on time.

The number of typographical errors in a document follows a Poisson distribution with a mean of 4 errors per page. Let X represent the number of errors on 2 pages. Find μx∗\mu _ { x ^ { * } }μx∗​

It is estimated that 35% of households own a riding lawn mower. A sample of 10 households is studied. What is the standard deviation of the number of households who own a riding lawn mower?

A coin is tossed until a head appears. Let X be the number of tosses. Is this a binomial distribution, and if so, what is the number of trials?

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

The following table presents the probability distribution of the number of vacations X taken last year for a randomly chosen family. Compute the mean $\mu _ { x }$ x 0 1 2 3 4 P(x) 0.06 0.66 0.16 0.09 0.03

The number of typographical errors in a document follows a Poisson distribution with a mean of 4 errors per page. Let X represent the number of errors on 2 pages. Find $\sigma _ { x }$

The number of typographical errors in a document follows a Poisson distribution with a mean of 4 errors per page. Let X represent the number of errors on 2 pages. Find $\mu _ { x ^ { * } }$