- #1

- 55

- 3

## Homework Statement

Suppose that X ~ N(μ,σ). Find

*a*in terms of μ and σ if P(X>a) = 1/3 * P(X ≤a)

## Homework Equations

## The Attempt at a Solution

1 - P(X ≤a) = 1/3 * P(X ≤a)

3 = 4P(X ≤a)

P(X ≤a) = 3/4

Since x

_{0}= μ + σz

_{0}where x

_{0}and z

_{0}are the same percentile for N(μ,σ) and N(0,1) (respectively), then z

_{0}= 0.67449 (by invNorm(0.75, 0, 1)). It follows that

a = μ + 0.67449σ

I'm not sure if this is the correct method, someone in my class solved it another way and got a different answer, but this seems to make sense to me.

Regards,

Michael