Question 1

If p = .5 and n = 4,then the corresponding binomial distribution is

Accepted Answer

A) Right skewed 
B) Left skewed 
C) Symmetric 
D) Bimodal

Question 2

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) .2552 
D) .8000

Question 3

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 at least 4 but no more than 8 patients arriving in a three-hour period.

Accepted Answer

A) .3813 
B) .5711 
C) .4276 
D) .7861 
E) .6174

Question 4

The Securities and Exchange Commission has determined that the number of companies listed in NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month. Find the probability that no more than one bankruptcy occurs next month.

Accepted Answer

A) .1931 
B) .9257 
C) .7326 
D) .4816 
E) .2674

Question 5

Whenever p = .5,the binomial distribution will _________ be symmetric.

Accepted Answer

A) Always 
B) Sometimes 
C) Never

Question 6

Determine the probability that a 3 will appear twice,if a fair die is rolled 10 times.

Accepted Answer

A) .5010 
B) .2907 
C) .2318 
D) .0065

Question 7

Two characteristics/assumptions of the Poisson distribution include:

Accepted Answer

A) Probability of success remains constant from trial to trial and the random variable of interest is continuous. 
B) The event occurring in one interval is independent of the event occurring in any other non-overlapping interval,and the random variable of interest is continuous. 
C) The event occurring in one interval is independent of the event occurring in any other non-overlapping interval,and the random variable of interest is discrete. 
D) The event occurring in one interval is dependent of the event occurring in any other non-overlapping interval,and the random variable of interest is continuous.

Question 8

The Post Office has established a record in a major Midwestern city for delivering 90% of its local mail the next working day.Calculate the standard deviation of the number delivered when 8 local letters are mailed.

Accepted Answer

A) .85 
B) .72 
C) 2.68 
D) 2.83

Question 9

Of all individual tax returns,37% include errors made by the taxpayer.If IRS examiners 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)   
B)   
C)   
D)

Question 10

If X has the probability distribution  compute the expected value of X.

Accepted Answer

A) 1.0 
B) 0.3 
C) 0.7 
D) 0.5

Question 11

For a binomial process,the probability of success is 40% and the number of trials is 5. Find the P(X = 2).

Accepted Answer

A) .2304 
B) .3456 
C) .3072 
D) .5760

Question 12

Historical data for a local steel manufacturing company shows that the average number of defects per standard sheet of steel is 2.In addition,the number of defects per unit is distributed according to Poisson distribution. Determine the standard deviation of the number of defective units for 32 sheets of metal.

Accepted Answer

A) 2 
B) 32 
C) 64 
D) 8

Question 13

The mean of the binomial distribution is np(1-p).

Accepted Answer

A) True 
 B)False

Question 14

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw,how much would you expect to win on average?

Accepted Answer

A) $3 
B) $2 
C) $6 
D) $9

Question 15

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) .6123 
B) .1709 
C) .1611 
D) .3662 
E) .3223

Question 16

According to data from the state blood program,40% of all individuals have group A blood.If six (6)individuals give blood,find the probability At least 3 of the individuals have group A blood.

Accepted Answer

A) .8208 
B) .5443 
C) .4557 
D) .1792

Question 17

For a binomial process,the probability of success is 40% and the number of trials is 5. Find the expected value.

Accepted Answer

A) 5.0 
B) 1.2 
C) 2.0 
D) 1.1

Question 18

The equation for the variance of the binomial distribution is given by:

Accepted Answer

A) px (1 - p)n-x 
B) np 
C) np (1-p) 
D)

Question 19

If x is a Poisson random variable with a mean of 10,what is the probability that x is greater than 6?

Accepted Answer

A) .9329 
B) .7797 
C) .8698 
D) .0002

Question 20

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: Find the probability that x (number of jobs finished on time)is within one standard deviation of the mean.

Accepted Answer

A) .6867 
B) .7483 
C) .5506 
D) .8844

Exam 5: Discrete Random Variables

If p = .5 and n = 4,then the corresponding binomial distribution is

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.

The Securities and Exchange Commission has determined that the number of companies listed in NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month. Find the probability that no more than one bankruptcy occurs next month.

Whenever p = .5,the binomial distribution will _________ be symmetric.

Determine the probability that a 3 will appear twice,if a fair die is rolled 10 times.

Two characteristics/assumptions of the Poisson distribution include:

The Post Office has established a record in a major Midwestern city for delivering 90% of its local mail the next working day.Calculate the standard deviation of the number delivered when 8 local letters are mailed.

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

If X has the probability distribution compute the expected value of X.

For a binomial process,the probability of success is 40% and the number of trials is 5. Find the P(X = 2) .

The mean of the binomial distribution is np(1-p).

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads) . If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw,how much would you expect to win on average?

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?

According to data from the state blood program,40% of all individuals have group A blood.If six (6) individuals give blood,find the probability At least 3 of the individuals have group A blood.

For a binomial process,the probability of success is 40% and the number of trials is 5. Find the expected value.

The equation for the variance of the binomial distribution is given by:

If x is a Poisson random variable with a mean of 10,what is the probability that x is greater than 6?

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: Find the probability that x (number of jobs finished on time) is within one standard deviation of the mean.