Question

The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 70 inches and a standard deviation of 10 inches. What is the probability that the mean annual snowfall during 25 randomly picked years will exceed 72.8 inches? Write your answer as a decimal rounded to 4 places.

Answer 1

Given,

= 70, = 10

Using central limit theorem,

P( < x) = P( Z < x - / ( / sqrt(n) ) )

So,

P( > 72.8) = P( Z > 72.8 - 70 / 10 / sqrt(25 ) )

= P( Z > 1.4)

= 1 - P( Z < 1.4)

= 1 - 0.9192 (Probability calculated from Z table)  

= 0.0808