Math- Statistics (see below)

Question

A machine packs nails in cartons. The number of nails in a carton is approximately normally distributed with a mean of 700.5 and a standard of deviation of 20. Find the probability that a carton of nails has more than 690 nails.

Answer 1

Prob ( X>690) = 1 - Prob ( X < 690) =

1 - Prob ( z < (690-700.5)/20)

= 1 - Prob ( z < -0.525)

= 1 - 0.299792

= 0.700208

or just over 70%