Question 1

Twenty coins are tossed.What is the probability of getting exactly 10 heads?

Accepted Answer

A) .3364 
B) .1602 
C) .5000 
D) .1762

Question 2

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 3

The expected value of the discrete random variable x is the population mean.

Accepted Answer

A) True 
 B)False

Question 4

Which of the following is not a discrete random variable?

Accepted Answer

A) The number of times a light changes red in a 10-minute cycle. 
B) The number of minutes required to run 1 mile. 
C) The number of defects in a sample selected from a population of 100 products. 
D) The number of criminals found in a five-mile radius of a neighborhooD.

Question 5

During off hours,cars arrive at a tollbooth on the East-West toll road at an average rate of 0.5 cars per minute.The arrivals are distributed according to the Poisson distribution.What is the probability that during the next five minutes,three cars will arrive?

Accepted Answer

A) .2138 
B) .1804 
C) .0126 
D) .0613

Question 6

According to data from the state blood program,40 percent of all individuals have group A blood.Suppose that of six randomly selected individuals,three have group A blood.Would you believe the data from the state blood program?

Accepted Answer

A) Yes,probability is > .05 
B) Yes,probability is < .05 
C) No

Question 7

The hypergeometric probability distribution can be approximated by the Poisson distribution.

Accepted Answer

A) True 
 B)False

Question 8

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.If X = the number of arrivals per minute,find the probability of 10 customers or fewer arriving within a minute.

Accepted Answer

A) .9998 
B) .9990 
C) .0008 
D) .0498

Question 9

The requirement that the probability of success remains constant from trial to trial is a property of the _________________ distribution.

Accepted Answer

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

Question 10

A discrete variable that can often be used to describe the number of occurrences of an event over a specified interval of time or space is a ___________ random variable.

Accepted Answer

A) Poisson 
B) Discrete 
C) Hypergeometric 
D) Continuous

Question 11

A company manufactures an appliance,gives a warranty and 95 percent of its appliances do not require repair before the warranty expires.If an organization buys 10 of these appliances,calculate an interval that contains 95.44 percent of all the appliances that won't require repair.

Accepted Answer

A)  $\left[ \begin{array} { l l } 
8.12 & 10.88
\end{array} \right]$ 
B)  $\left[ \begin{array} { l l } 
7.43 & 11.57
\end{array} ]\right.$ 
C)  $[ 8.81 \quad 10.19 ]$ 
D)  $\left[ \begin{array} { l l } 
8.55 & 10.45
\end{array} \right]$

Question 12

If the probability of a success on a single trial is .2,what is the probability of obtaining 3 successes in 10 trials if the number of successes is binomial?

Accepted Answer

A) .0031 
B) .5033 
C) .1074 
D) .2013

Question 13

Assume the number of trucks passing an intersection has a Poisson distribution with mean of 5 trucks per minute.What is the probability of 0 or 1 trucks in one minute?

Accepted Answer

A) .0404 
B) .0337 
C) .0842 
D) .0067

Question 14

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

Accepted Answer

A) True 
 B)False

Question 15

A discrete random variable may assume a countable number of outcome values.

Accepted Answer

A) True 
 B)False

Question 16

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that only 1 supports increased spending on environmental issues.

Accepted Answer

A) .0330 
B) .1318 
C) .3560 
D) .7844

Question 17

The property of expected values says if a and b are constants,and if x and y are random variables,then μ(ax + by) = aμx + bμy + 2ab.

Accepted Answer

A) True 
 B)False

Question 18

A large disaster cleaning company estimates that 30 percent of the jobs it bids on are finished within the bid time.Looking at a random sample of 8 jobs that it 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

Question 19

The binomial experiment consists of n independent,identical trials,each of which results in either success or failure and is such that the probability of success on any trial is the same.

Accepted Answer

A) True 
 B)False

Question 20

Two characteristics,or assumptions,of the Poisson distribution are:

Accepted Answer

A) The 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 on the event occurring in any other non-overlapping interval,and the random variable of interest is continuous.

Exam 5: Discrete Random Variables

Twenty coins are tossed.What is the probability of getting exactly 10 heads?

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

The expected value of the discrete random variable x is the population mean.

Which of the following is not a discrete random variable?

During off hours,cars arrive at a tollbooth on the East-West toll road at an average rate of 0.5 cars per minute.The arrivals are distributed according to the Poisson distribution.What is the probability that during the next five minutes,three cars will arrive?

According to data from the state blood program,40 percent of all individuals have group A blood.Suppose that of six randomly selected individuals,three have group A blood.Would you believe the data from the state blood program?

The hypergeometric probability distribution can be approximated by the Poisson distribution.

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.If X = the number of arrivals per minute,find the probability of 10 customers or fewer arriving within a minute.

The requirement that the probability of success remains constant from trial to trial is a property of the _________________ distribution.

A discrete variable that can often be used to describe the number of occurrences of an event over a specified interval of time or space is a ___________ random variable.

A company manufactures an appliance,gives a warranty and 95 percent of its appliances do not require repair before the warranty expires.If an organization buys 10 of these appliances,calculate an interval that contains 95.44 percent of all the appliances that won't require repair.

If the probability of a success on a single trial is .2,what is the probability of obtaining 3 successes in 10 trials if the number of successes is binomial?

Assume the number of trucks passing an intersection has a Poisson distribution with mean of 5 trucks per minute.What is the probability of 0 or 1 trucks in one minute?

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

A discrete random variable may assume a countable number of outcome values.

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that only 1 supports increased spending on environmental issues.

The property of expected values says if a and b are constants,and if x and y are random variables,then μ_{(ax + by)} = aμ_x + bμ_y + 2ab.

A large disaster cleaning company estimates that 30 percent of the jobs it bids on are finished within the bid time.Looking at a random sample of 8 jobs that it has contracted,find the probability that x (number of jobs finished on time) is within one standard deviation of the mean.

The binomial experiment consists of n independent,identical trials,each of which results in either success or failure and is such that the probability of success on any trial is the same.

Two characteristics,or assumptions,of the Poisson distribution are: