Question

Tire Kingdom installs automobile tires on a first-come-first-served basis. A random sample of 40 customers experienced an average wait time of 90.5 minutes. Assume that the standard deviation of the total wait time for all customers is 20.6 minutes. Determine the 90% confidence interval for this sample.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 90.5

Population standard deviation =    = 20.6

Sample size = n =40

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2    * ( /n)

= 1.645 * ( 20.6 /  40 )

= 5.358
At 90% confidence interval for this sample
is,

- E < < + E

90.5 - 5.358 <   < 90.5 + 5.358

85.142 <   < 95.858

( 85.142 , 95.858)