A brewery's filling machine is adjusted to fill bottles with a mean of 31.5 oz. of ale and a variance of 0.003. Periodically, a bottle is checked and the amount of ale noted.

Question

A brewery's filling machine is adjusted to fill bottles with a mean of 31.5 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 31.55 oz? (Give your answer correct to four decimal places.)

(b) Let's say you buy 100 bottles of this ale for a party. How many bottles would you expect to find containing more than 31.55 oz. of ale? (Round your answer up to the nearest whole number.)
  bottles

Reiny · Answer

remember that variance = (sd)^2
sd = √.003 = .0548

z-score = (31.55-31.5)/.0548 = .91241
so from the table or graph we see
the BELOW 31.55 would be .8192
so above would be 1 - .8192 = .1808

b) number of bottles = .1808(100) = appr 18

DeeDee7 · Answer

thank you, but b part says it is wrong at 18 and I repeated what you done and got 18.08 which rounds to 18. so not sure why wrong?? but the formula will help with the next ones

Tom 6 · Answer

There is a few of us working on these together so if you see different names that means none of us can figure it out. Again thank you