# Probability Distributions

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Question 1: Fifty-three percent of the population possesses characteristic X. If 15 people are randomly selected from the population, what is the probability that exactly 9 possess characteristic X?

a) .2009

b) .1653

c) .1780

d) .1102

Question2: A researcher is interviewing groups of 15 people to determine how many of them have degrees in business. The data gathered will most likely be outcomes from a:

a) continuous random variable

b) discrete random variable

c) education random variable

d) interviewed random variable

Question 3: If the following binomial problem is approximated by the Poisson distribution, the probability is: Prob(x = 4 n = 600 and p = .011)

a) .0661

b) .1076

c) .1295

d) .1673

Question 4: Customers arrive randomly at a small boutique at a rate of 2.6 every ten minutes. What is the probability that exactly 3 customers arrive in a five-minute interval?

a) .0319

b) .0687

c) .9711

d) .0998

Question 5: The combinations part of the binomial formula compute the:

a) sample space

b) probability of a success

c) probability of a single sequence

d) number of sequences

Question 6: A discrete distributions that is used to describe the occurrence of rare events is:

a) binomial

b) Poisson

c) Hypergeometric

d) Chi-square

Question 7: In a binomial experiment, p is .83. If n = 12, what is the probability that x = 10?

a) 0.3277

b) 0.1784

c) 0.296

d) 0.2203

Question 8 : Consider the following discrete random distribution. What is the mean of the distribution?

a) 2.48

b) 0.85

c) 1.97

d) 1.26

Question 9: The graph of the binomial distribution, n = 20 and p = .50 is:

a) skewed right

b) skewed left

c) approximately symmetrical

d) bimodal

Question 10: There are 15 people in the job applicant pool. Ten of the people in the applicant pool wear glasses. If 4 people are randomly hired from the applicant pool, what is the probability that none of the people hired wear glasses?

a) 0.3409

b) 0.2748

c) 0.2133

d) 0.0037

Question 11: In a binomial experiment, p is .29 and n = 18. What is the standard deviation of this binomial distribution?

a) 1.925

b) 1.046

c) 2.129

d) 3.425

Question 12: Consider the following discrete random distribution. What is the standard deviation of the distribution?

a) 1.3619

b) 1.1701

c) 1.0063

d) 1.2648

Question 13: In a binomial experiment, p is .30. If n = 10, what is the probability that 2 <= 5?

a) 0.348

b) 0.5274

c) 0.803

d) 0.9127

Question 14: Perhaps the most widely known of all discrete distributions is the:

a) hypergeometric distribution

b) binomial distribution

c) normal distribution

d) Poisson distribution

Question 15: The office receptionist receives, on average, 2.43 calls every half hour. What is the probability that in a twenty-minute interval, the receptionist receives exactly 2 calls?

a) 0.3015

b) 0.2597

c) 0.2017

d) 0.1852

Question 16: There are 15 people in the job applicant pool. Ten of the people in the pool wear glasses. If 4 people are randomly hired from the applicant pool, what is the probability that exactly 3 wear glasses?

a) 0.4396

b) 0.3763

c) 0.2985

d) 0.2209

Question 17: The Poisson distribution can be used to approximate binomial distributions problems if:

a) n< 20 and n? p<= 7

b) n> 20 and n? p<= 7

c) n> 20 and n? p>=7

d) n< 20 and n? p>= 7

Question 18: Consider the following discrete random distribution. What is the variance of the distribution?

a) 1.56

b) 2.09

c) 1.37

d) 1.04

Question 19: Customers arrive randomly at a small boutique at a rate of 2.6 every ten minutes. What is the probability that more than 6 customers arrive in a ten-minute interval?

a) 0.232

b) 0.0171

c) 0.0653

d) 0.0982

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Answers Multiple Choice questions on Probability Distributions

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Question 1 Multiple Choice

Fifty-three percent of the population possesses characteristic X. If 15 people are randomly selected from the population, what is the probability that exactly 9 possess characteristic X?

0.2009

0.1653

0.178

0.1102

Answer: 0.178

This is Binomial distribution

Binommial distribution

P(r)= ncr p r * q n-r

n= 15

p= 0.53

q=1-p= 0.47

r= 9

P(r)= ncr p r * q n-r =

r=

9 P(9)= 0.1780 =5005*(0.53^9)*(0.47^6)

Question 2 Multiple Choice

A researcher is interviewing groups of 15 people to determine how many of them have degrees in business. The data gathered will most likely be outcomes from a:

continuous random variable

discrete random variable

education random variable

interviewed random variable

Answer: discrete random variable

Question 3 Multiple Choice

If the following binomial problem is approximated by the Poisson distribution, the probability is: Prob(x = 4

n = 600 and p = .011)

0.0661

0.1076

0.1295

0.1673

Answer: 0.1076

Poisson distribution:

P(x)= lambda x e -lambda / x!

where

P(x)= probability of x

lambda = average

Here

lambda = 6.6 =600*0.011

x=

4 P(4)= 0.1076 or 10.76%

Question 4 Multiple Choice

Customers arrive randomly at a small boutique at a rate of 2.6 every ten minutes.

What is the probability that exactly 3 customers arrive in a five-minute interval?

0.0319

0.0687

0.9711

0.0998

Answer: 0.0998

This is

Poisson distribution:

P(x)= lambda x e -lambda / x!

where

P(x)= probability of x

lambda = average

Here

lambda = 1.3 =2.6*(5/10)

x=

3 P(3)= 0.0998 or 9.98%

Question 5 Multiple Choice

The combinations part of the binomial formula compute the:

sample space

probability of a success

probability of a single sequence

number of sequences

Answer: number of sequences

Question 6 Multiple Choice

A discrete ...

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