Q4.

(i).Incomes in a certain town are approximately normally distributed with a mean of $36,000 and a standard deviation of $7,000. A random sample of 75 households is taken. What is the probability that the sample mean is greater than $37,000?

[ Hint: find the mean and standard deviation of the sample mean first and use the z-score formula to find your probability]

Soln.

(ii).The contents of bottles of beerare normally distributed with a mean of 300 and a standard deviation of 5ml. if a six (6) pack is randomly selected, what is the probability that its total content exceeds 1776 ml?

[ Hint: First, find the sample mean X_bar.,then find the mean and standard deviation of the sample mean and use the z-score formula to find your probability]

Soln.