Question

PLEASE SHOW THE WORK

In a normal model with a mean of 100 and standard deviation of 16, what cutoff value bounds

1. The highest 5%?
2. The lowest 30%?
3. The middle 80%?

Answer 1

Solution :

Using standard normal table ,

a.

P(Z > z) = 5%

1 - P(Z < z) = 0.05

P(Z < z) = 1 - 0.05

P(Z < 1.65) = 0.95

z = 1.65

Using z-score formula,

x = z * +

x = 1.65 * 16 + 100 = 126.4

cutoff value bounds is 126.4

b.

P(Z < z) = 30%

P(Z < -0.52) = 0.3

z = -0.52

Using z-score formula,

x = z * +

x = -0.52 * 16 + 100 = 91.68

cutoff value bounds is 91.68

c.

Middle 80% as the to z values are -1.282 and 1.282

Using z-score formula,

x = z * +

x = -1.282 * 16 + 100 = 79.49

and

x = 1.282 * 16 + 100 = 120.51

Two values are 79.49 and 120.51