Question

Assume a normal distribution of items with a mean of 682 and a standard deviation of 103. 75.17% of all items are below what value? Round to the nearest one decimal place

Answer 1

Given

We have the 17th percentile. We need to find the z-score associated to this percentile. We have to solve the following equation

P( Z < z)=0.17

The value of z that solves the equation above cannot be made directly, it solved either by looking at a standard normal distribution table . It is found that that the solution is z= - 0.954

Now, using the z-score formula , we can compute the point x below which 17% of all the items lie.

Hence, 17% of all items are below 583.0