Question

Use the normal distribution of fish lengths for which the mean is 8 inches and the standard deviation is 2 inches. Assume the variable x is normally distributed.

(A) what percent of the fish are longer than 12 inches?

(B) if 400 fish are randomly selected, how many would you expect to be shorter than 7 inches?

Answer 1

Here' the answer to the question with full concept. Please don't hesitate to give a "thumbs up" in case you're satisfied with the answer. We know tha params of normal distribution as

Mean = 8 inches

Dev = 2 inches

a. P(X>12) = P(Z> 12 -8/2) = P(Z>2) = .023. So, 2.3% of fishes are longer than 12 inches

b. P(X<7) = P(Z< 7-8/2) = P(Z<-.5) = 1-.6915 = .3085 or 30.85% of fishes have shorter than 7 inches length. This is 400*.3085 = 123.4 or approximately 123 fishes