Question

Given the mean of a random variable, X, is 10 and P(X < 11) = 0.67. Find the standard deviation.

Answer 1

Explanation:

This is the problem we need to solve:

`z=\frac{x_i-\bar{x}}{\sigma}` and we have everything but the z-score (which we find from a table) with our main unknown being the standard deviation.

If the probability that a random variable that is less than 11 is .67, we first have to find the z-score from the table that is closest to .67, and there are 2:

P(z < .43) = .66640 and P(z < .44) = .67003

We'll use z = .44

`.44=(11-10)/(\sigma)` and

`.44=(1)/(\sigma)` and

`\sigma=(1)/(.44)` so

σ = 2.27 (check it; it works!)