Melons from a certain large distributor have diameters thatfollow an approximately normal distribution with a mean of 133millimeters (mm) and a standard deviation of 5 mm.
a. If a melon from this distributor is randomly selected,calculate the probability that the melon will have a diameter thatis greater than 137 mm.
b. Calculate the diameter of a melon such that 15 percent ofthis distributor’s melons have a larger diameter.
c. Suppose a customer randomly selects melons from thisdistributor’s inventory until he obtains a melon with a diameterthat is greater than 137 mm. Calculate the probability that thefirst such melon is the fourth melon that the customer selects.
d. Suppose five melons are randomly selected from thisdistributor’s inventory and that the diameter of each selectedmelon is recorded.
Calculate the mean and the standard deviation of the samplingdistribution of the mean diameter for random samples of fivemelons.
Calculate the probability that the mean diameter for a randomsample of five melons is greater than 137 mm.
