Question

the mid term exam had a normal distribution with mean 70 and standard deviation 10. to get a C you have to be in the middle 40% of the class. which two grades will define the middle 40%.

Answer 1

Solution:

Middle 40%

Middle 40% as the z value are

= 1 - 40%

= 1 - 0.4 = 0.6

/ 2 = 0.6 / 2 = 0.3

1 -   / 2 = 1 - 0.3 = 0.7

Z _0.3 = -0.524

Z _0.7 = 0.524

Using z-score formula,

x = z * +

x = -0.524 * 10 + 70 = 64.76

and

x = 0.524 * 10 + 70 = 75.24

Two grades will define the middle 40%.is 64.76 and 75.24