Question

A3. A Retailing Entrepreneur sells sophisticated running shoes whose weights are assumed to be
normally distributed with a mean of 12 grammes and a standard deviation of 0.5 grammes.
(a) What is the probability that a shoe weighs more than 13 grammes? [3]
(b) What must the standard deviation of weight be in order for the company to state that
99.9% of its shoes are less than 13 grammes? [6]
(c) If the standard deviation remains at 0.5 grammes, what must the mean weight be in
order for the company to state that 99.9% of its shoes are less than 13 grammes? [5]

Answer 1

(a) Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability that relates to the Z score.

(b,c) Reverse process from proportion to Z score. Insert into above equation and solve.