Question 2 The diameter of hail hitting the ground during a

Question 2: The diameter of hail hitting the ground during a storm is normally distributed with a mean of 0.6 inch and a standard deviation of 0.1 inch. What is the probability that

a)   A hailstone picked up at random will have a diameter greater than 0.75 inch?

b)   By the end of the storm, what proportion of the hailstones would have had diameters greater than 0,65 inch?

c)   If 10 hailstones are picked up at random, what is the probability that there are 2 hailstones with diameters greater than 0.65?

Solution

a) Mean=0.6

S.D=0.1

Z=(0.75-0.6)/0.1=0.015

Corresponding z is:1-0.75=0.25

b) n=2

z=(0.65-0.6)/0.1/sqrt(2)=.707

corresponding p is:1-0.065=0..935

c) Z=(0.75-0.6)/0.1=0.015