Question

Scores on a test are normally distributed with a mean of 81 and a standard deviation of 8. Find the probability that a randomly chosen score will be less than 70? Show your work.

Answer 1

In order to find the probability, first let's calculate the z-score for x = 70, using the formula below:

`\begin{gathered} z=(x-\mu)/(\sigma)\\ \\ z=(70-81)/(8)\\ \\ z=-(11)/(8)\\ \\ z=-1.375 \end{gathered}`

Now, let's look at the z-table for the probability that corresponds to z = -1.375.

Looking at the z-table, for z = -1.375 we have p = 0.0845.

Therefore we have:

`P(x<70)=P(z<-1.375)=0.0845=8.45\%`