Question

For a test whose scores are normally distributed, with mean 470 and standard deviation 52, what is the cutoff score separating the bottom 11% of the test scores from the rest (that is, the score so that 11% of all scores are below this score)?

Answer 1

We will employ the z score table in this problem.

The shaded part is our area of interest.We will be required to seek the value of the z score at 0.11.

when we ahave a probability of 0.11 or 11%

This corresponds with a z-score of -1.225.

We then substitute into our z-score equation:

`z=(x-\mu)/(\sigma)`

where

Therefore, we have

`\begin{gathered} x=\sigma z+\mu \\ x=52(-1.225)+470 \\ x=406.3 \end{gathered}`