Question

SHOW WORK!

The scores on two standardized tests are normally distributed.
The first test had a mean of 56 and a standard deviation of 6.
The second test had a mean of 76 and a standard deviation of 6.
What score would you need on the second test to equal a score of 70 on the first test?
Give answer to the nearest whole number.

Answer 1

Calculating the z score for the first test:

$Z = \frac{X - \mu}{\sigma} = \frac{70-56}{6} = \frac{7}{3}=2.3333$

Now we have to find Y such that:

$Z = \frac{Y - \mu}{\sigma} = \frac{Y-76}{6} = \frac{7}{3}$

$\rightarrow \frac{Y-76}{6} = \frac{7}{3}$

$\rightarrow Y = 90$

Hence 90 score would be needed on the second test to equal a score of 70 on the first test.

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