A survey of 250 lobster fishermen found that they catch an a

A survey of 250 lobster fishermen found that they catch an average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?

Solution

Here expected value is 32 and standard deviation of 4. Sample size is 36 people So probability that their average catch is less than 31.5 pounds is = P (x < 31.5) = P (z < ((31.5-32)/(4/sqrt(36))) = P (z < -0.75) = 0.226627352