he diameter of oranges from a Florida orchard are normally d

he diameter 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 for oranges and needs to know the average diameter for a random sample of 8 oranges. If a random sample of 8 oranges is to be taken from this orchard, what is the probability that the mean diameter of these oranges will be smaller than 3 inches?

Solution

So the probability that the mean diameter of these oranges will be smaller than 3 inches is

P(xbar>3) = P((xbar-mean)/(s/vn) >(3-3.2)/(1.1/sqrt(8)))

=P(Z>-0.51)

=0.6950 (from standard normal table)