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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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