Question: The diameters of oranges from a Florida orchard are normally distributed with mean \[\mu =3.2\] inches and standard deviation \[\sigma =1.1\] inches. A packing supplier is designing special occasion presentation boxes of oranges and needs to know the average diameter for a random sample of 36 oranges. What is the probability that the mean diameter \[\bar{x}\] for these oranges is

(a) smaller than 3 inches.

(b) larger than 4 inches.

(c) between 3 and 4 inches.