Question

Problem 6. Let x be a normally distributed random variable with unknown mean µ and a standard deviation of 10. The 99-th percentile is 58.3 Find µ.

Answer 1

Solution:
Given in the question
Population mean =
Population standard deviation() = 10
Also given 99th percentile is 58.3
So P-value = 0.99
From Z table or standard normal distribution table we found z-score
Z-score = 2.33
Also Z-score can be calculated as
Z-score = (X - )/
So Population mean can be calculated as
Population mean () = X - Z-score* = 58.3 - 2.33*10 = 58.3 - 23.3 = 35
So Population mean = 35