Answer to Question #306925 in Statistics and Probability for noone

Question

D. The result of the nationwide aptitude test in mathematics are normally distributed with a mean of 70 and a standard deviation of 5. Find the raw score such that 60% of the cases are below it and case above it.

Answer 1

We are given that 60% of the scores will be below the score.

From the standard normal table we find the critical value z = 0.25

By using the formula:

z = $\frac{X-\mu}{\sigma}$

Given $\mu$ = 70, $\sigma$ = 5 and z = 0.25

0.25 = $\frac{X-70}{5}$

we solve for the unknown score X

5(0.25) = X - 70

1.25 = X-70

X=1.25+70 = 71.25

X=71.25

Which is approximately equal to 71

Answer: The raw score = 71