In some questions you are asked to find the mean μ or the standard deviation σ or both from a Normal Distribution when given the probabilities of being greater than or less than an observed value.

Here you will find all the different scenarios.

## Finding the mean, μ

Example:

- If X ~ N( μ, 9 ) Given P( X > 5 ) = 0.4. Find μ.

Example:

- If X ~ N( μ, 25 ) and the 30th percentile is 18. Find μ.

## Finding the standard deviation, σ.

Example:

- If X ~ N( 12, σ
^{2}) Given P( X > 6 ) = 0.85. Find σ.

## Finding two unknowns μ and σ

Example:

- A high jumper knows from experience that she can clear a height of at least 1.65m on 7 out of 10 attempts and clear a height of at least 1.78m once in 5 attempts.

Assuming that the height she jumps in cm is given by the r.v. X and is normally distributed.

Find to 1 decimal place the mean and standard deviation of the heights the jumper can reach.