Question 1

Where n = 150 is the number of trials and p = 0.6 is the probability of success in each trial, the standard deviation of a binomial experiment is 36.

Accepted Answer

A) True 
 B)False  False

Question 2

A warehouse contains six parts made by company A and ten parts made by company B. If four parts are selected at random from the warehouse, the probability that none of the four parts is from company A is approximately 0.1154.

Accepted Answer

A) True 
 B)False  True

Question 3

What does the binomial distribution formula do?

Accepted Answer

A)   It computes the number of permutations of x successes (and, therefore, n - x failures)  that can be achieved in n trials of a random experiment that satisfies the conditions of the binomial experiment.
B)   It computes the probability of x successes in n trials of a random experiment that satisfies the conditions of a binomial experiment.
C)   It produces one of two possible outcomes, conventionally called success and failure.
D)   It produces the probability of x successes when a random sample of size n is drawn without replacement from a population of size N within which M units have the characteristic that denotes success. B

Question 4

For a binomial experiment with n trials, p is the probability of success, q is the probability of failure, and x is the number of successes in n trials. Which one of the following statements is NOT a property of such an experiment?

Accepted Answer

A)   p + q = 1
B)   = 1 for x = 0, 1, . . ., n
C)   P(x = 0)  =
D)   P(x = 1)  =

Question 5

Automobile Spark Plugs Narrative
An eight-cylinder automobile engine has two misfiring spark plugs. The mechanic removes all four plugs from one side of the engine.
-Refer to Automobile Spark Plugs Narrative. What is the probability the two misfiring spark plugs are among those removed?

Accepted Answer

The answer of Automobile Spark Plugs Narrative
An eight-cylinder automobile engine...

Question 6

Automobile Service Centre Narrative
An automobile service centre can take care of eight cars per hour. Assume that the cars arrive at the service centre randomly and independently of each other at a rate of six per hour, on average.
-Refer to Automobile Service Centre Narrative. What is the probability that fewer than two cars will be in the service centre at any point during a given hour?

Accepted Answer

The answer of Automobile Service Centre Narrative
An automobile service centre...

Question 7

Toll Station Narrative
It is known that between 8 and 10 a.m. on Saturdays, cars arrive at a certain toll station at a rate of 60 per hour. Assume that a Poisson process is occurring and that the random variable x represents the number of cars arriving at the station between 9:00 and 9:05 a.m.
-Refer to Toll Station Narrative. What is the standard deviation of the number of cars arriving at the toll station between 9:00 and 9:05 a.m.?

Accepted Answer

The answer of Toll Station Narrative
It is known that between...

Question 8

The number of teleport inquiries, x, in a timesharing computer system averages 0.2 per millisecond and follows a Poisson distribution.
a. Find the probability that no inquiries are made during the next millisecond.
b. Find the probability that no inquiries are made during the next three milliseconds.

Accepted Answer

The answer of The number of teleport inquiries, x, in...

Question 9

It is known that in an Introductory Statistics class of 20 students, 70% of them own smartphones. If you were to randomly pick 10 students from that class, what is the probability that 70% of those picked would have smartphones?

Accepted Answer

The answer of It is known that in an Introductory...

Question 10

Warehouse Narrative
A warehouse contains ten computer printers, four of which are defective. A company randomly selects five of the ten printers to purchase.
-Refer to Warehouse Narrative. What is the variance of x?

Accepted Answer

The answer of Warehouse Narrative
A warehouse contains ten computer printers,...

Question 11

Which of the following distributions could NOT be used to describe the exact distribution for a discrete random variable?

Accepted Answer

A)   binomial distribution
B)   Poisson distribution
C)   hypergeometric distribution
D)   normal distribution

Question 12

Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time or space is 1.5, then what is P(x = 2)?

Accepted Answer

A)   0.5020
B)   0.2510
C)   0.2231
D)   0.01116

Question 13

Which of the following experiments CANNOT be modelled by a Poisson distribution?

Accepted Answer

A)   the number of calls received by a switchboard during a given period of time
B)   the number of bacteria per small volume of fluid
C)   the gender of individuals going through a security check at an airport in a given hour
D)   the number of customer arrivals at a checkout counter during a given minute

Question 14

Automobile Service Centre Narrative
An automobile service centre can take care of eight cars per hour. Assume that the cars arrive at the service centre randomly and independently of each other at a rate of six per hour, on average.
-Refer to Automobile Service Centre Narrative. What is the probability that exactly six cars will be in the service centre at any point during a given hour?

Accepted Answer

The answer of Automobile Service Centre Narrative
An automobile service centre...

Question 15

A warehouse contains six parts made by company A and ten parts made by company B. If four parts are selected at random from the warehouse, the probability that all four parts are from company B is approximately 0.008.

Accepted Answer

A) True 
 B)False

Question 16

Let x be a binomial random variable with n = 20 and p = 0.05.
a. Calculate  using the cumulative binomial probabilities table in Appendix I of your text. 
b. Use the Poisson approximation to calculate  
c. Compare the results of (a) and (b). Is the approximation accurate?

Accepted Answer

The answer of Let x be a binomial random variable...

Question 17

When sampling without replacement, which of the following is the appropriate probability distribution to use?

Accepted Answer

A)   the binomial distribution
B)   the hypergeometric distribution
C)   the Poisson distribution
D)   the normal approximation to the binomial distribution

Question 18

What kinds of probabilities does the hypergeometric probability distribution provide?

Accepted Answer

A)   It provides probabilities associated with possible values of a binomial random variable in situations in which sampling is done without replacement.
B)   It provides probabilities associated with possible values of a binomial random variable in situations in which the probability of success changes from one trial to the next.
C)   both a and b
D)   neither a or b

Question 19

Bicycle Repair Shop Narrative
The number of people arriving at a bicycle repair shop follows a Poisson distribution, with an average of five arrivals per hour. Let x represent number of people arriving per hour.
-Refer to Bicycle Repair Shop Narrative. What is the probability that between four and nine people, inclusively, arrive at the bike repair shop in a one-hour period?

Accepted Answer

The answer of Bicycle Repair Shop Narrative
The number of people...

Question 20

Scholarship Narrative
A college has seven applicants for three scholarships: four females and three males. Suppose the seven applicants are equally qualified and no preference is given by the selection committee for choosing either gender. Let x equal the number of female students chosen for the three scholarships.
-Refer to Scholarship Narrative. What is the mean of the distribution of x?

Accepted Answer

The answer of Scholarship Narrative
A college has seven applicants for...

Exam 5: Several Useful Discrete Distributions