Question

Test scores in Mr. Smith's Stats class are normally distributed with a mean of 76 and a standard deviation of 10. Mr. Smith declared that 11.5% of his class didn't perform well on the test. What test score is at the upper limit of his test scores that didn't perform well on the test? (Meaning what is the test score that corresponds to the beginning bad grades on Mr. Smith's test.) Round to the nearest whole test grade.

Answer 1

Given that,

mean = = 76

standard deviation = =10

Using standard normal table,

P(Z > z) = 11.5%

= 1 - P(Z < z) = 0.115

= P(Z < z ) = 1 - 0.115

= P(Z < z ) = 0.885

= P(Z < 1.20 ) = 0.885

z =1.20 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.20 *10+76

x= 88