Question

The weights of individuals in some populations are known to follow a normal distribution with the mean 175 pounds. If 70% of individuals are heavier than 167 pounds, then what is the population standard deviation of weight?

Answer 1

Given the, mean (μ) = 175 pounds and 70% of individuals are heavier than 167 pounds. That means, P(X > 167) = 0.70

We want to find, the population standard deviation

First we find, z-score such that,

P(Z > z) = 0.70

=> 1 - P(Z < z) = 0.70

=> P(Z < z) = 0.30

Using standard normal z-table we get, z-score corresponding probability of 0.30 is z = -0.52

So, for z = -0.52, we find the population standard deviation,

=> Population standard deviation = 15.38