Question

Suppose that your statistics professor tells you that the scores on a midterm exam were approximately normally distributed with a mean of 78 and a standard deviation of 7. The top 15% of all scores have been designated A’s. What is the minimum score that you must earn in order to receive a letter grade A.

Answer 1

Given that,

mean = = 78

standard deviation = =7

Using standard normal table,

P(Z > z) = 15%

= 1 - P(Z < z) = 0.15

= P(Z < z ) = 1 - 0.15

= P(Z < z ) = 0.85

= P(Z <1.04 ) = 0.85

z =1.04 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.04 *7+78

x= 85.28

x=85