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

Sagot :

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:

[tex]z=\frac{x-m}{g}[/tex]

So we have:

[tex]\begin{gathered} z_1=\frac{66-78}{8}=-1.5 \\ z_2_{}=\frac{90-78}{8}=1.5 \end{gathered}[/tex]

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:

[tex]\begin{gathered} P=1-0.0668-0.0668 \\ P=0.8664=86.64\text{\%} \end{gathered}[/tex]

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