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 X ¯ represents the average amount of snowfall in 35 years, find k such that P(X ¯ <k) = 0.75. Round your answer to 3 decimal places.

Answer 1

Given that,

mean = = 70

standard deviation = = 10

n = 35

= 70

= / n = 10 /35=1.6903

Using standard normal table,

P(Z < z) = 0.75

= P(Z < z) = 0.75

= P(Z <0.67 ) = 0.75

z = 0.67    Using standard normal table,

Using z-score formula  

= z * +   

= 0.67*1.6903+70

=71.133