Statistics and Probability

Question

Assume the random variable X is normally distributed with a mean = 50 and standard deviation = 7. Find the 96th percentile.

Answer 1

Per the table, Prob ( z < ) = 0.96 = 96%

x = 1.750686*7+50

Answer 2

In order to complete this problem, you'll usually use either a calculator or a normal distribution table. By doing this, you'll find that the z-score associated with the 96th percentile is 1.751.

I can then find the desired value using the formula:

x = mean + z-score * standard deviation

x = 50 + 1.751 * 7

x = 62.257

There are several websites that you can use in order to complete calculations like this if you don't have a device available.