Question

The annual rainfall (in inches) in a certain region is normally distributed with mean μ = 40 inches and standard deviation σ = 4 inches. What is the probability that, starting with this year, it will take over 10 years before a year occurs having a rainfall of over 50 inches? What assumptions are you making?

Answer 1

0.005826

Explanation:

Given that the annual rainfall (in inches) in a certain region is normally distributed with mean μ = 40 inches and standard deviation σ = 4 inches

We have each year is independent of the other and there are two outcomes

p = Probability for a particular year to have rainfall of over 50 inches

=P(X>50)

= 1-0.9938

=0.0062

P(X<50) = 0.9938

Reqd probability

= P(X<50) for 10 years * P(X>50) on 11th year

=
`(0.9938)^(10) *0.0062\\=0.005826`

Assumptions we made:

Each year is independent of the other.