Question

The annual rainfall in a certain region is approximately normally distributed with mean 42.4 inchesand standard deviation 5.9 inches. Round answers to the nearest tenth of a percent.a) What percentage of years will have an annual rainfall of less than 44 inches? %b) What percentage of years will have an annual rainfall of more than 38 inches? %c) What percentage of years will have an annual rainfall of between 37 inches and 43 inches?%Question 11

Answer 1

In a normal distribution with mean μ and standard deviation σ, the z-score of a measure X is given by:

Z = X - μ

σ

mean = 42.4 inches, hence μ = 42.8 inches

standard deviation = 5.9, hence σ = 5.9

(a)

The proportion is the p-value of Z when X = 44, so:

Z = X - μ

σ

Z = 44 - 42.4

5.9

Z = 1.6/5.9

Z = 0.27

Z = 0.27 has a p-value of 0.6064

0.6064 x 100% = 60.64

60.64 of years will have an annual rainfall of less than 44 inches