Question

Fishermen fishing for spiny lobster are allowed to keep only lobsters with a carapace length of 3.25 inches or longer. (Than carapace length is measured from the rear edge of the eye socket to the rear edge of the body shell.) Any lobster smaller than 3.25 inches must be returned to the sea. Suppose that lobster carapace lengths have a distribution that is mound shaped and approximately symmetric with a mean of 5.50 inches and a standard deviation of 2.25 inches. Approximately what proportion of lobsters will have to be returned to the sea

Answer 1

16%

Explanation:

First we start by solving for the z score

We have the following information

x = 3.25

Standard deviation = sd = 2.25

Mean = 5.50

Z = (x - mean)/sd

z = 3.25 - 5.50/2 25

z = -1.00

If we look this up in the standard normal distribution table,

P(z<-1.00) = 0.1587

Which when approximated gives us

16%

Therefore approximately 16% of lobsters will have to be returned back to the sea.