Answer to Question #65388 in Statistics and Probability for shweta

Question

A bank wishing to determine the average amount of time a customer must wait to be served took a random sample of 100 customers and found that the mean waiting time was 2.7 minutes. Assuming that the population standard deviation is known to be 15 minutes, find the %90 confidence interval estimate of the mean waiting time for all the bank’s customers.

Answer 1

Due to the central limit theorem distribution of the sum of stochastic variables converges to the normal distribution.
Therefore, it is possible to approximate the solution with the normal distribution.
The formula for the confidence interval will be:
(mean - z_(1-alpha/2) * sd / sqrt(n), mean - z_(1-alpha/2) * sd / sqrt(n))
where mean = 2.7, sd = 15
z_(1 - alpha) = 1.645
n = 100