Answer to Question #152275 in Statistics and Probability for Ruwan

Question

The annual rainfall in a certain area is normally distributed with a mean of 25 inches and a standard deviation of 5 inches. The following questions ask you to compute probabilities and quintiles from a normal distribution.
a. What is the probability the area receives at least 30 inches of rain in a year?
b. What is the probability the area receives between 15 and 30 inches of rain in a year?
c. What is the probability the area receives at most 20 inches of rain in a year?

Answer 1

μ = 25

σ = 5

a.

$P(X≥30)=P(\frac{X-μ}{σ}≥ \frac{30-25}{5}) \\ = P(Z≥1) \\ = P(Z≤-1) \\ = 0.1587$

b.

$P(15≤X≤30)=P(\frac{15-25}{5}≤\frac{X-μ}{σ}≤\frac{30-25}{5}) \\ = P(-2≤) \\ = P(Z≤1) - P(Z≤-2) \\ = 0.8413-0.0228 \\ = 0.8186$

c.

$P(X≤20) = P(\frac{X-μ}{σ}≤ \frac{20-25}{5}) \\ =P(Z≤-1) \\ = 0.1587$