The monthly electrical utility bills of all customers for the Far East Power and Light Company are known to be distributed as a normal distribution with mean equal to $87.00 a month and standard deviation of $36.00. If a statistical sample of n = 100 customers is selected at random, what is the probability that the mean bill for those sampled will exceed $75.00?
A) -0.33
B) Approximately 0.63
C) About 1.00
D) 3.33

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean will also be normally distributed with mean $87.00 and standard deviation $36.00/sqrt(100) = $3.60. To find the probability that the sample mean exceeds $75.00, we calculate the z-score: (75 - 87) / 3.60 = -3.33. The probability of a z-score greater than -3.33 is approximately 1.00.

The Monthly Electrical Utility Bills of All Customers for the Far