Question

A set of final examination grades in an introductory statistics course was found to be normally distributed with a mean of 73 and a standard deviation of 8. The probability is 60% that a student taking the test scores higher than what grade?

a. 0.7257

b. 0.0521

c. 71

d. 0.9479

e. 75

Answer 1

solution

Using standard normal table,

P(Z > z) = 60%

= 1 - P(Z < z) = 0.60

= P(Z < z ) = 1 - 0.60

= P(Z < z ) = 0.40

= P(Z < -0.25 ) = 0.40  

z = -0.25 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= -0.25*8+73

x= 71