Question

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?

Answer 1

Solution :

Given that,

mean = = 25 minutes.

standard deviation = = 11 minutes.

A) n = 40

=   = 25 minutes.

= / n = 11 / 40 = 1.74

P( > 27) = 1 - P( < 27)

= 1 - P[( - ) / < (27 - 25) / 1.74]

= 1 - P(z <1.15)

Using z table,    

= 1 - 0.8749

= 0.1251

B) n = 75

= = 25 minutes.

= / n = 11/ 75 = 1.27

P(23 < < 26)  

= P[(23 - 25) /1.27 < ( - ) / < (26 - 25) / 1.27 )]

= P(-1.57 < Z < 0.79)

= P(Z < 0.79) - P(Z < -1.57)

Using z table,  

= 0.7852 - 0.0582   

= 0.7270

C) n = 100

=   = 25 minutes.

= / n = 11/ 100 = 1.1

P( 24) = P(( - ) / (24 - 25) / 1.1)

= P(z 0.91)

Using z table

= 0.8186