The manufacturer of a coffee dispensing machine claims that

The manufacturer of a coffee dispensing machine claims that the ounces per cup dispensed is mound shaped and symmetric with mean mu = 7 ounces and standard deviation sigma = 0.8 ounce. If 40 cups of coffee are measured, what is the probability that the average ounces per cup is between 6.8 and 7.4 ounces?

Solution

So the probability that the average ounces per cup is between 6.8 and 7.4 ounces is

P(6.8<xbar<7.4)

=P((6.8-7)/(0.8/sqrt(40)) <(xbar-mean)/(s/vn) < (7.4-7)/(0.8/sqrt(40)))

=P(-1.58<Z<3.16)

=0.9422 (from standard normal table)