Question

1.            The mean wait time at Social Security Offices is 25 minutes with a standard deviation of 11 minutes. Use this information to answer the following questions:

A.            If you randomly select 40 people what is the probability that their average wait time will be more than 27 minutes?

B.            If you randomly select 75 people what is the probability that their average wait time will be between 23 and 26 minutes?

C.            If you randomly select 100 people what is the probability that their average wait time will be at most 24 minutes?

2.            The proportion of people who wait more than an hour at the Social Security Office is 28%. Use this information to answer the following questions:

A.            If you randomly select 45 people what is the probability that at least 34% of them will wait more than an hour?

B.            If you randomly select 60 people what is the probability that between 25% and 30% of them will wait more than an

hour?

C.            If you randomly select 150 people what is the probability that less than 23% of them will wait more than an hour?

Answer 1

1. The mean wait time at Social Security Offices is 25 minutes with a standard deviation of 11 minutes. Use this information to answer the following questions:

A. If you randomly select 40 people what is the probability that their average wait time will be more than 27 minutes?

As the sample sizes here are greater than 30

We can assume normality

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/(s.d/√n)

Given mean = 25

S.d = 11

P(x>27)

Z = (27-25)/(11/√40) = 1.15

From z table, P(z>1.15) = 0.1251

B)

N = 75

P(23<x<26) = p(x<26) - p(x<23)

P(x<26)

Z = (26-25)/(11/√75) = 0.79

From z table, P(z<0.79) = 0.7852

P(x<23)

Z = (23-25)/(11/√75) = -1.57

From z table, P(z<-1.57) = 0.0582

Required probability is 0.7852 - 0.0582 = 0.727

C)

N = 100

P(x<24)

Z = (24-25)/(11/√100) = -0.91

From z table, P(z<-0.91) = 0.1814