Question

Score on a test are normally distributed with a mean of 63.2 and standard deviation of 11.7 find, P 81 which separates the bottom81% from top 19%

Answer 1

P 81 = 73.5

Explanation:

This is a normal distribution problem with a mean of 63.2 and standard deviation of 11.7.

Let the number that separates the bottom 81% from the top 19% be x' and let it's z-score be z'.

P(x ≤ x') = P(z ≤ z') = 0.81

Using the normal distribution table,

z' = 0.878

But note that the z-score for any value is that value minus the mean divided by standard deviation.

z' = (x' - μ)/σ

0.878 = (x' - 63.2)/11.7

x' = 73.4726 = 73.5 to 1 d.p

Hope this Helps!!!