Question

Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of and a standard deviation of 0.04 ounce. Find the probability that the bottle contains fewer than of beer.

Answer 1

I suppose this is full question you want to ask.

Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.16 and a standard deviation of 0.04 ounce. Find the probability that the bottle contains fewer than 12.06 of beer.

Explanation:

Hypothesized Mean u = 12.16 oz, Standard Deviation (SD) = 0.04

z score = (x - u) / SD

where x = 12.06

z score = (12.06 - 12.16)/0.04= -2.5oz

normal cdf (-1E99, -2.5)= 0.0062096

P(x <12.06)= P(z<-2.5) = 0.062