Question

The scores on two standardized tests are normally distributed. The first test had a mean of 58 and a standard deviation of 6. The second test had a mean of 78 and a standard deviation of 5. What score would you need on the second test to equal a score of 66 on the first test? Give answer to the nearest whole number.

Answer 1

84.67

Explanation:

Given that :

First test:

Mean (m) = 58

Standard deviation (s) = 6

A score of 66 on the first test :

Z score (standardized score) :

Z = (66 - 58) / 6

Zscore = 1.3333

Second test:

Mean (m) = 78

Standard deviation (s) = 5

Using the Zscore pertaining to 66 in the first test :

Z = (x - m) / s

1.3333 = (x - 78) / 5

1.3333 * 5 = x - 78

6.66667 = x - 78

x = 6.6667 + 78

x = 84.67