In: Statistics and Probability
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.
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