A brewery\'s filling machine is adjusted to fill bottles with a mean of 33.2 oz.

Question

A brewery's filling machine is adjusted to fill bottles with a mean of 33.2 oz. of ale and a variance of 0.003. Periodically, a bottle is checked and the amount of ale noted.

(a) Assuming the amount of fill is normally distributed, what is the probability that the next randomly checked bottle contains more than 33.30 oz? (Give your answer correct to four decimal places.)

(b) Let's say you buy 92 bottles of this ale for a party. How many bottles would you expect to find containing more than 33.30 oz. of ale? (Round your answer up to the nearest whole number.)

Explanation / Answer

Mean = 33.2

Sd = sqrt (0.003) = 0.055

A) P(X > 33.3) = P(Z > (33.3-33.2)/0.055)

= P(Z > 1.82)

= 1 - P(Z < 1.82)

= 1 - 0.9656

= 0.0344

B) n = 92

Expected value = 92 * 0.0344 = 3.16 = 3

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