Over next 5 years, what is the probability that there are two years having a rainfall of less than 35 inches?

Question

The annual rainfall (in inches) in a certain region is normal distributed with mu = 40, sigma = 4. Over next 5 years, what is the probability that there are two years having a rainfall of less than 35 inches?

Answer 1

The probability that rainfall in one year is less than 35 inches is p=0.10565.

The probability that there are two years having a rainfall of less than 35 inches is

[(5!) / (2! * 3!)] * p² * (1-p)³ = 10 * 0.10565² * 0.89435³ = 0.079848
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http://www.math.csusb.edu/faculty/stanton/m262/normal_distribution/normal_distribution.html
http://en.wikipedia.org/wiki/Binomial_distribution
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Answer 2

Each year is an independent event.

P (rainfall less than 35 inches in a year) is associated with a z-score of (35 - 40) / 4 = -5/4 = -1.25

This corresponds to P = .1056

I'm too tired to continue. The guy above looks to have done it right.