Question

Installation of a certain hardware takes a random amount of time with a standard deviation of 5 minutes. A computer technician installs this hardware on 64 different computers, with the average installation time of 42 minutes. Compute a 90% confidence interval for the mean installation time.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 42

Population standard deviation = =5

Sample size = n = 64

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

Z/2 = Z_{0.05 = 1.645}

Z/2 = 1.645

Margin of error = E = Z/2* ( /n)

= 1.645 * (5 / 64)

= 1.03

At 90% confidence interval estimate of the population mean is,

- E < u < + E

2-1.03 < u < 42 +1.03

40.97< u < 43.03

( 40.97,43.03)