Question

A Statistics exam has mean m=78 in standard deviation of g=8 estimate the portion of Grades between 66 and 90

Answer 1

In order to estimate the portion of grades between 66 and 90, first let's find the z-score for these two values, using the formula:

`z=(x-m)/(g)`

So we have:

`\begin{gathered} z_1=(66-78)/(8)=-1.5 \\ z_2_{}=(90-78)/(8)=1.5 \end{gathered}`

Looking at the z-table, a z-score of 1.5 corresponds to a z-value of 0.0668.

Since we have this z-value from the left and right, the percentage we want is:

`\begin{gathered} P=1-0.0668-0.0668 \\ P=0.8664=86.64\text{\%} \end{gathered}`