Question

Use the normal distribution of fish lengths for which the mean is 11 inches and the standard deviation is 5 inches. assume the variable x is normally distributed. left parenthesis a right parenthesis what percent of the fish are longer than 14 ​inches? left parenthesis b right parenthesis if 500 fish are randomly​ selected, about how many would you expect to be shorter than 9 ​inches?

Answer 1

27.43% of the fish will be longer than 14 inches.

All we need to do is find the z-score and then the percent.

(14 - 11) / 5 = 0.6 which gives a percent of 27.43% over this amount.

For the fish shorter than 9 inches:
(9 - 11) / 5 = -0.4 which gives a percent of 34.46% under this amount.

34.46% of 500 is about 172 fish.