Question 1

Answer the question.
-Spinning a roulette wheel 3 times, keeping track of the winning numbers.

Accepted Answer

A) Not binomial: the trials are not independent. 
B) Procedure results in a binomial distribution. 
C) Not binomial: there are too many trials. 
D) Not binomial: there are more than two outcomes for each trial. 
A) Not binomial: the trials are not independent. 
B) Procedure results in a binomial distribution. 
C) Not binomial: there are too many trials. 
D) Not binomial: there are more than two outcomes for each trial.

Question 2

Solve the problem.
-Find the variance for the given probability distribution. $$\begin{array} { c | c } 
\mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.17 \
\hline 1 & 0.28 \
\hline 2 & 0.05 \
\hline 3 & 0.15 \
\hline 4 & 0.35
\end{array}$$

Accepted Answer

A) 2.63 
B) 7.43 
C) 2.69 
D) 2.46 
A) 2.63 
B) 7.43 
C) 2.69 
D) 2.46

Question 3

In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?

Accepted Answer

A) 0.0547 
B) 0.9846 
C) 0.913 
D) 0.9815 
A) 0.0547 
B) 0.9846 
C) 0.913 
D) 0.9815

Question 4

Provide an appropriate response.
-Identify each of the variables in the Binomial Probability Formula. $P ( x ) = \frac { n ! } { ( n - x ) ! x ! } \cdot p ^ { x } \cdot q ^ { n - x }$
Also, explain what the fraction $\frac { n ! } { ( n - x ) ! x ! }$ computes.

Accepted Answer

n is the fixed number of trials, x is th

Question 5

Provide an appropriate response.
-Sampling without replacement involves dependent events, so this would not be considered a binomial experiment. Explain the circumstances under which sampling without replacement could be considered independent and, thus, binomial.

Accepted Answer

When the sample size

Question 6

Suppose that computer literacy among people ages 40 and older is being studied and that the accompanying tables describes the probability distribution for four randomly selected people, where x is the number that are computer literate. Is it unusual to find four computer literates among four randomly selected people? $$\begin{array} { c | c } 
x & P ( x ) \
\hline 0 & 0.16 \
\hline 1 & 0.25 \
\hline 2 & 0.36 \
\hline 3 & 0.15 \
\hline 4 & 0.08
\end{array}$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 7

Use the normal distribution to approximate the desired probability.
-Find the probability of selecting 12 or more girls.

Accepted Answer

A) 0.001 
B) 0.007 
C) 0.006 
D) 0.022 
A) 0.001 
B) 0.007 
C) 0.006 
D) 0.022

Question 8

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
-$$n = 4 , x = 3 , p = \frac { 1 } { 6 }$$

Accepted Answer

A)  $0.0154$ 
B)  $0.0039$ 
C)  $0.0116$ 
D)  $0.0231$ 
A)  $0.0154$ 
B)  $0.0039$ 
C)  $0.0116$ 
D)  $0.0231$

Question 9

An airline estimates that 98% of people booked on their flights actually show up. If the airline books 76 people on a flight for which the maximum number is 74, what is the probability that the number of people who show up will exceed the capacity of the plane?

Accepted Answer

A) 0.8051 
B) 0.3340 
C) 0.2154 
D) 0.5494 
A) 0.8051 
B) 0.3340 
C) 0.2154 
D) 0.5494

Question 10

Use the normal distribution to approximate the desired probability.
-Find the probability of selecting exactly 8 girls.

Accepted Answer

A) 0.183 
B) 0.000 
C) 0.022 
D) 0.122 
A) 0.183 
B) 0.000 
C) 0.022 
D) 0.122

Question 11

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
-$$\rho = \frac { 1 } { 6 }$$ n = 6, x = 3,

Accepted Answer

A) 0.0536 
B) 0.0154 
C) 0.0322 
D) 0.0286 
A) 0.0536 
B) 0.0154 
C) 0.0322 
D) 0.0286

Question 12

Assume that a probability distribution is described by the discrete random variable x that can assume the values 1, 2, . . . , n; and those values are equally likely. This probability has mean and standard deviation described as follows: $$\mu = \frac { \mathrm { n } + 1 } { 2 } \text { and } \sigma = \sqrt { \frac { \mathrm { n } ^ { 2 } - 1 } { 12 } }$$ Show that the formulas hold for the case of n = 7.

Accepted Answer

\[\begin{array} { l } 
\mu = \sum [ x \c

Question 13

A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

Accepted Answer

A) 0.055 
B) 0.945 
C) 0.117 
D) 0.172 
A) 0.055 
B) 0.945 
C) 0.117 
D) 0.172

Question 14

Identify the given random variable 
-The number of oil spills occurring off the Alaskan coast

Accepted Answer

A) Discrete 
B) Continuous 
A) Discrete 
B) Continuous

Question 15

Solve the problem.
-In a certain town, 40% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults)who have a college degree. Find the standard deviation for the probability distribution. $$\begin{array} { c | c } 
\mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.1296 \
\hline 1 & 0.3456 \
\hline 2 & 0.3456 \
\hline 3 & 0.1536 \
\hline 4 & 0.0256
\end{array}$$

Accepted Answer

A) 0.96 
B) 1.12 
C) 1.88 
D) 0.98 
A) 0.96 
B) 1.12 
C) 1.88 
D) 0.98

Question 16

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied.
-If a person is randomly selected from a certain town, the probability distribution for the number, x, of siblings is as described in the accompanying table. $$\begin{array} { c | c } 
\mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.27 \
1 & 0.29 \
2 & 0.23 \
3 & 0.10 \
4 & 0.08 \
5 & 0.02
\end{array}$$

Accepted Answer

Not a probability di

Question 17

Solve the problem.
-A 28-year-old man pays $57 for a one-year life insurance policy with coverage of $100,000. If the probability that he will live through the year is 0.9992, what is the expected value for the insurance policy?

Accepted Answer

A) -$56.95 
B) $99,920.00 
C) $23.00 
D) $80.00 
A) -$56.95 
B) $99,920.00 
C) $23.00 
D) $80.00

Question 18

Provide an appropriate response.
-List the two requirements for a probability histogram. Discuss the relationship between the sum of the probabilities in a probability distribution and the total area represented by the bars in a probability histogram.

Accepted Answer

The sum of the probabilities i

Question 19

Solve the problem.
-The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4521, 0.3970, 0.1307, 0.0191, and 0.0010, respectively. Find the variance for the probability distribution.

Accepted Answer

A) 0.59 
B) 0.77 
C) 1.11 
D) 0.51 
A) 0.59 
B) 0.77 
C) 1.11 
D) 0.51

Question 20

Use the given values of n and p to find the minimum usual value µ - 2? and the maximum usual value µ + 2?
-$$n = 604 , p = \frac { 4 } { 7 }$$

Accepted Answer

A) Minimum: 369.47; maximum: 320.82 
B) Minimum: 320.82; maximum: 369.47 
C) Minimum: 332.98; maximum: 357.31 
D) Minimum: 298.57; maximum: 391.72 
A) Minimum: 369.47; maximum: 320.82 
B) Minimum: 320.82; maximum: 369.47 
C) Minimum: 332.98; maximum: 357.31 
D) Minimum: 298.57; maximum: 391.72

Answer the question. -Spinning a roulette wheel 3 times, keeping track of the winning numbers.

Solve the problem. -Find the variance for the given probability distribution. () 0 0.17 1 0.28 2 0.05 3 0.15 4 0.35

In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?

Provide an appropriate response. -Identify each of the variables in the Binomial Probability Formula. $P ( x ) = \frac { n ! } { ( n - x ) ! x ! } \cdot p ^ { x } \cdot q ^ { n - x }$ Also, explain what the fraction $\frac { n ! } { ( n - x ) ! x ! }$ computes.

Provide an appropriate response. -Sampling without replacement involves dependent events, so this would not be considered a binomial experiment. Explain the circumstances under which sampling without replacement could be considered independent and, thus, binomial.

Use the normal distribution to approximate the desired probability. -Find the probability of selecting 12 or more girls.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $n = 4 , x = 3 , p = \frac { 1 } { 6 }$

An airline estimates that 98% of people booked on their flights actually show up. If the airline books 76 people on a flight for which the maximum number is 74, what is the probability that the number of people who show up will exceed the capacity of the plane?

Use the normal distribution to approximate the desired probability. -Find the probability of selecting exactly 8 girls.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $\rho = \frac { 1 } { 6 }$ n = 6, x = 3,

A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

Identify the given random variable -The number of oil spills occurring off the Alaskan coast

Solve the problem. -A 28-year-old man pays $57 for a one-year life insurance policy with coverage of $100,000. If the probability that he will live through the year is 0.9992, what is the expected value for the insurance policy?

Provide an appropriate response. -List the two requirements for a probability histogram. Discuss the relationship between the sum of the probabilities in a probability distribution and the total area represented by the bars in a probability histogram.

Solve the problem. -The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4521, 0.3970, 0.1307, 0.0191, and 0.0010, respectively. Find the variance for the probability distribution.

Use the given values of n and p to find the minimum usual value µ - 2? and the maximum usual value µ + 2? - $n = 604 , p = \frac { 4 } { 7 }$

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Normal Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Multinomial Experiments and Contingency Tables

Analysis of Variance

Nonparametric Statistics

Statistical Process Control

Filters

Exam 5: Probability Distributions

Answer the question. -Spinning a roulette wheel 3 times, keeping track of the winning numbers.

Solve the problem. -Find the variance for the given probability distribution. () 0 0.17 1 0.28 2 0.05 3 0.15 4 0.35

In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?

Provide an appropriate response. -Sampling without replacement involves dependent events, so this would not be considered a binomial experiment. Explain the circumstances under which sampling without replacement could be considered independent and, thus, binomial.

Use the normal distribution to approximate the desired probability. -Find the probability of selecting 12 or more girls.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - n=4,x=3,p=16n = 4 , x = 3 , p = \frac { 1 } { 6 }n=4,x=3,p=61​

An airline estimates that 98% of people booked on their flights actually show up. If the airline books 76 people on a flight for which the maximum number is 74, what is the probability that the number of people who show up will exceed the capacity of the plane?

Use the normal distribution to approximate the desired probability. -Find the probability of selecting exactly 8 girls.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - ρ=16\rho = \frac { 1 } { 6 }ρ=61​ n = 6, x = 3,

A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

Identify the given random variable -The number of oil spills occurring off the Alaskan coast

Solve the problem. -A 28-year-old man pays $57 for a one-year life insurance policy with coverage of $100,000. If the probability that he will live through the year is 0.9992, what is the expected value for the insurance policy?

Provide an appropriate response. -List the two requirements for a probability histogram. Discuss the relationship between the sum of the probabilities in a probability distribution and the total area represented by the bars in a probability histogram.

Solve the problem. -The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4521, 0.3970, 0.1307, 0.0191, and 0.0010, respectively. Find the variance for the probability distribution.

Use the given values of n and p to find the minimum usual value µ - 2? and the maximum usual value µ + 2? - n=604,p=47n = 604 , p = \frac { 4 } { 7 }n=604,p=74​

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Normal Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Multinomial Experiments and Contingency Tables

Analysis of Variance

Nonparametric Statistics

Statistical Process Control

Filters

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $n = 4 , x = 3 , p = \frac { 1 } { 6 }$

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $\rho = \frac { 1 } { 6 }$ n = 6, x = 3,

Use the given values of n and p to find the minimum usual value µ - 2? and the maximum usual value µ + 2? - $n = 604 , p = \frac { 4 } { 7 }$