Question 1

Which of the following distributions can be used to solve the following problem?
The average number of cars arriving at a drive-thru fast food restaurant is 3 in ten minutes,what is the probability that exactly 4 cars will arrive in a five minute interval?

Accepted Answer

A) Binomial 
B) Poisson 
C) Hypergeometric 
D) Normal 
E) Uniform

Question 2

Of all individual tax returns,37% include errors made by the taxpayer.If tax auditors are assigned randomly selected returns in batches of 12,find the mean and standard deviation for the number of erroneous returns per batch.

Accepted Answer

A)  $\mu$ = 2.80, $\sigma$ = 1.67 
B)  $\mu$ = 3.70, $\sigma$ = 1.67 
C)  $\mu$ = 4.44, $\sigma$ = 1.67 
D)  $\mu$ = 4.44, $\sigma$ = 2.80 
E)  $\mu$ = 7.56, $\sigma$ = 2.80

Question 3

The number of ways to arrange x successes among n trials is equal to

Accepted Answer

A)  $n / x!$ 
B)  $\frac { n ! } { ( n - x ) ! }$ 
C)  $n / x$ 
D)  $n ! / x !$ 
E)  $\frac { n ! } { x ! ( n - x ) ! }$

Question 4

A fair die is rolled 10 times.What is the probability that an odd number (1,3,or 5)will occur less than 3 times?

Accepted Answer

A) 0547 
B) 1172 
C) 1550 
D) 7752 
E) 8450

Question 5

An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that:
-At least 3 troubles will be repaired on the same day.

Accepted Answer

The answer of An important part of the customer service...

Question 6

If the probability distribution of X is:
$$\begin{array} { c c } 
\mathrm { X } & \mathrm { P } ( \mathrm { X } ) \
3 & 1 / 8 \
4 & 1 / 8 \
5 & 3 / 8 \
6 & 3 / 8
\end{array}$$
-What is the variance of X?

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 4 
E) 5

Question 7

The manager of the local grocery store has determined that, on the average, 4 customers use the service desk every half-hour. Assume that the number of customers using the service desk has a Poisson distribution.
-What is the probability that during a randomly selected half-hour period exactly 2 customers use the service desk?

Accepted Answer

A) 0183 
B) 0733 
C) 1465 
D) 9084 
E) 7619

Question 8

In a binomial experiment,the results of one trial are dependent on the results of other trials.

Accepted Answer

A) True 
 B)False

Question 9

A multiple-choice test has 30 questions and each one has five possible answers,of which one is correct.If all answers were guesses,find the probability of getting exactly four correct answers.

Accepted Answer

A) 0604 
B) 1325 
C) 2000 
D) 2552 
E) 8000

Question 10

If you were asked to play a game in which you rolled two fair dice and were given $4 for every die that landed on six dots,how much would you expect to win on average?

Accepted Answer

The answer of If you were asked to play a...

Question 11

A large disaster cleaning company estimates that each of the jobs it bids on are finished within the bid time with probability 0.3 independent of each other job it bids on. Consider a random sample of 8 jobs that is has contracted.
-What is the mean number of jobs completed within the bid time?

Accepted Answer

A) 1.3 
B) 8.3 
C) 2.4 
D) 4.3 
E) 3.4

Question 12

An urn contains 50 black balls and 20 blue balls.If you select 30 balls at random,what is the probability that exactly 20 of them will be black balls?

Accepted Answer

A) 0.2581 
B) 0.3861 
C) 0.6667 
D) 0.1573 
E) 0.4770

Question 13

Would you accept or reject the claim? Explain.

Accepted Answer

The answer of Would you accept or reject the claim?...

Question 14

A fair die is rolled 10 times.What is the probability that an even number (2,4,or 6)will occur between 2 and 4 times?

Accepted Answer

A) 0.6123 
B) 0.1709 
C) 0.1611 
D) 0.3662 
E) 0.3223

Question 15

What is the variance for this distribution?

Accepted Answer

The answer of What is the variance for this distribution?...

Question 16

A large disaster cleaning company estimates that 30% of the jobs it bids on are finished within the bid time. Looking at a random sample of 8 jobs that is has contracted:
-Calculate the mean number of jobs completed within the bid time.

Accepted Answer

The answer of A large disaster cleaning company estimates that...

Question 17

Historical data shows that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours. Assume that the patient arrivals are distributed according to Poisson distribution.
-Determine the probability of 6 patients arriving in a five-hour period.

Accepted Answer

A) 019 
B) 136 
C) 233 
D) 369 
E) 401

Question 18

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.Write a formula for the probability of X,where X = the number of arrivals per minute.

Accepted Answer

The answer of Consider a Poisson distribution with an average...

Question 19

Which one of the following statements is not an assumption of the binomial distribution?

Accepted Answer

A) We sample without replacement from a small population. 
B) The experiment consists of n identical trials. 
C) The probability of success remains constant from trial to trial. 
D) Trials are independent of each other. 
E) Each trial results in one of two mutually exclusive outcomes.

Question 20

A fair die is rolled 36 times.What is the standard deviation of the even number (2,4,or 6)outcomes?

Accepted Answer

A) 18 
B) 9 
C) 5 
D) 3 
E) 1.732

Exam 4: Discrete Random Variables

Which of the following distributions can be used to solve the following problem? The average number of cars arriving at a drive-thru fast food restaurant is 3 in ten minutes,what is the probability that exactly 4 cars will arrive in a five minute interval?

Of all individual tax returns,37% include errors made by the taxpayer.If tax auditors are assigned randomly selected returns in batches of 12,find the mean and standard deviation for the number of erroneous returns per batch.

The number of ways to arrange x successes among n trials is equal to

A fair die is rolled 10 times.What is the probability that an odd number (1,3,or 5) will occur less than 3 times?

If the probability distribution of X is: $\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}$ -What is the variance of X?

In a binomial experiment,the results of one trial are dependent on the results of other trials.

A multiple-choice test has 30 questions and each one has five possible answers,of which one is correct.If all answers were guesses,find the probability of getting exactly four correct answers.

If you were asked to play a game in which you rolled two fair dice and were given $4 for every die that landed on six dots,how much would you expect to win on average?

A large disaster cleaning company estimates that each of the jobs it bids on are finished within the bid time with probability 0.3 independent of each other job it bids on. Consider a random sample of 8 jobs that is has contracted. -What is the mean number of jobs completed within the bid time?

An urn contains 50 black balls and 20 blue balls.If you select 30 balls at random,what is the probability that exactly 20 of them will be black balls?

Would you accept or reject the claim? Explain.

A fair die is rolled 10 times.What is the probability that an even number (2,4,or 6) will occur between 2 and 4 times?

What is the variance for this distribution?

A large disaster cleaning company estimates that 30% of the jobs it bids on are finished within the bid time. Looking at a random sample of 8 jobs that is has contracted: -Calculate the mean number of jobs completed within the bid time.

Historical data shows that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours. Assume that the patient arrivals are distributed according to Poisson distribution. -Determine the probability of 6 patients arriving in a five-hour period.

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.Write a formula for the probability of X,where X = the number of arrivals per minute.

Which one of the following statements is not an assumption of the binomial distribution?

A fair die is rolled 36 times.What is the standard deviation of the even number (2,4,or 6) outcomes?

Exam 4: Discrete Random Variables

Which of the following distributions can be used to solve the following problem? The average number of cars arriving at a drive-thru fast food restaurant is 3 in ten minutes,what is the probability that exactly 4 cars will arrive in a five minute interval?

Of all individual tax returns,37% include errors made by the taxpayer.If tax auditors are assigned randomly selected returns in batches of 12,find the mean and standard deviation for the number of erroneous returns per batch.

The number of ways to arrange x successes among n trials is equal to

A fair die is rolled 10 times.What is the probability that an odd number (1,3,or 5) will occur less than 3 times?

If the probability distribution of X is: XP(X) 31/841/853/863/8\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}X3456​P(X) 1/81/83/83/8​ -What is the variance of X?

In a binomial experiment,the results of one trial are dependent on the results of other trials.

A multiple-choice test has 30 questions and each one has five possible answers,of which one is correct.If all answers were guesses,find the probability of getting exactly four correct answers.

If you were asked to play a game in which you rolled two fair dice and were given $4 for every die that landed on six dots,how much would you expect to win on average?

A large disaster cleaning company estimates that each of the jobs it bids on are finished within the bid time with probability 0.3 independent of each other job it bids on. Consider a random sample of 8 jobs that is has contracted. -What is the mean number of jobs completed within the bid time?

An urn contains 50 black balls and 20 blue balls.If you select 30 balls at random,what is the probability that exactly 20 of them will be black balls?

Would you accept or reject the claim? Explain.

A fair die is rolled 10 times.What is the probability that an even number (2,4,or 6) will occur between 2 and 4 times?

What is the variance for this distribution?

A large disaster cleaning company estimates that 30% of the jobs it bids on are finished within the bid time. Looking at a random sample of 8 jobs that is has contracted: -Calculate the mean number of jobs completed within the bid time.

Historical data shows that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours. Assume that the patient arrivals are distributed according to Poisson distribution. -Determine the probability of 6 patients arriving in a five-hour period.

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.Write a formula for the probability of X,where X = the number of arrivals per minute.

Which one of the following statements is not an assumption of the binomial distribution?

A fair die is rolled 36 times.What is the standard deviation of the even number (2,4,or 6) outcomes?

If the probability distribution of X is: $\begin{array} { c c } \mathrm { X } & \mathrm { P } ( \mathrm { X } ) \\3 & 1 / 8 \\4 & 1 / 8 \\5 & 3 / 8 \\6 & 3 / 8\end{array}$ -What is the variance of X?