Question

Applicants for a correctional facility are required to take a Doll-Chang Emotional IQ exam and only the top 20% will be accepted. The population mean is 70 and the standard deviation is 11.

a. What score must an applicant get to be accepted?

b. If it was decided the top 40% were to be accepted, what score would someone have to get to be accepted?

Answer 1

Solution:-

Given that,

mean = = 70

standard deviation = = 11

a) top 20%

P(Z > z ) = 0.20

1- P(z < z) =0.20

P(z < z) = 1-0.20 = 0.80

z = 0.842

Using z-score formula,

x = z * +

x = 0.842* 11 + 70

x = 79.26

Answer = 79.26

b)

top 40%

P(Z > z ) = 0.40

1- P(z < z) =0.40

P(z < z) = 1-0.40 = 0.60

z = 0.253

Using z-score formula,

x = z * +

x = 0.253* 11 + 70

x = 72.78

Answer = 72.78