Assume the lengths of fish are normally distributed with mean 30 inches and standard deviation 3 inches.

a. Calculate the length such that 90% of fish are less than this length.

b. If you randomly sample five fish, what is the probability all five are less than the length calculated in part (a)?

c. A fish is defined as an outlier if it is shorter than 22 inches or longer than 38 inches. If you randomly sample one fish, what is the probability it is an outlier?

d. If you randomly sample 100 fish, what is the probability at least one is an outlier?