Statistics Homework Help!

Question

The diameter of of hail hitting the ground during a storm is normally distributed with a mean of .5 inch and a standard deviation of .1 inch.  What is the probability that:

 

A)  A hailstone picked up at random will have a diameter greater than .71 inch?

 

B) Two hailstones picked up in a row will have diameters greater than .6 inch? ( assume independence of the two diameters)

 

C) By the end of the storm, what proportion of the hailstones would have had diameters greater than .71 inch?

Answer 1

The hailstone diameters follow a normal distribution with an average of 0.5 inches and a standard deviation of 0.1 inches.

A) A diameter of 0.71 inches is a little more than two standard deviations above the mean. Only about 1.8 percent of hailstones are larger than this size. So, the probability that a randomly chosen hailstone has a diameter greater than 0.71 inches is about 0.018.

B) A diameter of 0.6 inches is one standard deviation above the mean. About 15.9 percent of hailstones are larger than 0.6 inches. Since the two hailstones are independent, the probability that both are larger than 0.6 inches is found by multiplying the probabilities. This gives about 2.5 percent, or 0.025.

C) The proportion of hailstones larger than 0.71 inches over the entire storm is the same as the probability in part A. So, about 1.8 percent of all hailstones would have diameters greater than 0.71 inches.