Math CentralQuandaries & Queries


Question from Lorie, a student:

3. The amount of annual snowfall in a certain mountain range is normally distributed with a mean of 109 inches, and a standard deviation of 10 inches.

a. What is the probability that the mean annual snowfall during 40 randomly picked years will exceed 111.8 inches?

Hi Lorie,

Let X be the amount of annual snowfall in inches then X is distributed as the normal random variable with μ = 109 and σ = 10. Let X-bar be the mean annual snowfall of n = 40 years then X-bar is distributed as the normal random variable with mean μX-bar = μ = 109 and variance σ2X-bar = σ2/n = 100/40. You want to find Pr(X-bar > 111.8).

You first need to convert X-bar to the standard normal distribution by Z = (X-bar - μ)/(σ/√n) and then evaluate Pr[(X-bar - μ)/(σ/√n) > (118 - μ)/(σ/√n)] = Pr(Z > (111.8 - 109)/(10/√40)]. Finally evaluate (111.8 - 109)/(10/√40) and use the standard normal table to evaluate the probability.


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS