When pearl oysters are opened pearls of various sizes are fo

When pearl oysters are opened, pearls of various sizes are found. Suppose that each oyster contains a pearl with a diameter that varies evenly from 0 to 10 mm. Let D be the diameter of the pearl.

a) Calculate the mean and standard deviation of the pearl diameter.

b) What percent of pearls have diameter no more than 7.5 mm?

c) What is the probability that a pearl has a diameter of exactly 5 mm?

d) The pearl oyster farmer wants to know the value of the upper 20% of the pearl diameters. Find this value.

e) Pearls with a diameter of at least 4 mm have commercial value. Calculate the probability that an oyster contains a pearl of commercial value.

f) Suppose that a farmer retrieves ten oysters out of the water. Let the random variable P represent the number of them containing pearls of commercial value. Find the probability at least 8 of the oysters the farmer retrieves contain pearls of commercial value. Indicate what distribution(s) and parameter(s) you are using. Assume the oysters grow pearls independently of one another.

Solution