Question

The amount of annual snowfall in a certain mountain range is normally distributed with a mean of 70 inches and a standard deviation of 10 inches. If represents the average amount of snowfall in 5 years, find k such that P(<k) = 0.85. Round your answer to 3 decimal places.

Answer 1

Given that,

mean = = 70

standard deviation = = 10

n = 5

= 70

= / n = 10/5=4.47

Using standard normal table,

P(Z < z) = 0.85

= P(Z < z) = 0.85

= P(Z < 1.04) = 0.85

z = 1.04 Using standard normal z table,

Using z-score formula  

= z * +   

= 1.04*4.47+70

= 74.649

k= = 74.649