Answer to Question #181171 in Statistics and Probability for Jiaying Liang

Question

Suppose the scores of students on a test are normally distributed with a mean score of 70 points and a standard deviation of 10 points. It is decided to give A’s to 10 percent of the students and B’s to 23 percent of the students. Find what scores should be assigned A’s and B’s.

Answer 1

mean = $\mu = 70$

standard deviation = $\sigma = 10$

Using standard normal table,

P(X > x) = 10%

$P(X>x) = 0.10 \\ 1 -P(X≤x) = 0.10 \\ P(X≤x) = 1 -0.10 = 0.90$

Using standard normal z table

$\frac{x-70}{10} = 1.29 \\ x -70 = 12.9$

x = 82.9 (score for A’s)

P(X > x) = 33% (top 33% = 10% for A’s+23 % for B’s)

$P(X > x ) = 0.33 \\ 1 -P(X≤x) = 0.33 \\ P(X≤x) = 1 -0.33 = 0.67$

Using standard normal z table

$\frac{x-70}{10} = 0.44 \\ x-70 = 4.4 \\$

x = 74.4 (score for B’s)