A new beer dispensing system is being installed at the Statm

A new beer dispensing system is being installed at the Statman Bar and Grill. The volume of beer dispensed by the system is known to be normally distributed with a standard deviation of 0.8 oz. The bar serves 16 oz. glasses of beer.

a) What is the probability that a glass overflows if the mean is 14 oz? Give your answer to 3 places

past the decimal without a leading zero.

b) What mean is required for only 2% of the glasses to overflow? Give your answer to two places

past the decimal.

c) Suppose now that the mean is known to be 14 oz. but the variance is unknown. What

variance is required so that only 2% of the glasses overflow? Give your answer to two places past

the decimal.

Solution

a standard deviation of 0.8 oz. Mean = 16 oz. glasses of beer.

a) P(X>14) = P(Z>2/0.4) = 0.00

b) P(X>x ) = 0.02

i.e. z = 2.05

x = 14+2.05(0.4) = 14.82

c) P(X>x) =0.02

0.02 = 16-14/s       = 2/s

s =2/0.02 = 100