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
