Sam is evaluting the service level provided to walkin custom

Sam is evaluting the service level provided to walk-in customers. Accordingly, his staff recorded the waiting time for 64 randomly selected walk-in customers & determined that their mean waiting time was 15 minutes. Assume that the population standard deviation is 4 minutes. The 90% confidence interval for the population mean of waiting times is:

A)14.18 to 15.82

B) 13.86 to 16.14

C) 14.27 to 15.73

D) 9.88 to 20.12

Solution

Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=15
Standard deviation( sd )=4
Sample Size(n)=64
Confidence Interval = [ 15 ± Z a/2 ( 4/ Sqrt ( 64) ) ]
= [ 15 - 1.64 * (0.5) , 15 + 1.64 * (0.5) ]
= [ 14.18,15.82 ]