Question

The test scores for the analytical writing section of the Graduate Record Examination can be approximated by a normal distribution with a mean of 155.69 and a standard deviation of 5.05.

a) What is the maximum score that can be in the bottom 11.4% of Scores?

b) Between what two values does the middle 74% lie?

c) What is the minimum score that can be in the top 4.5%

Answer 1

Given that,

mean = = 155.69

standard deviation = = 5.05

(a)

P(Z < -1.206) = 0.0.114

z = -1.206

Using z-score formula,

x = z * +

x = -1.206 * 5.05 + 155.69 = 149.60

score = 149.60

(b)

The middle 74% has the z values : -1.13 . +1.13

Using z-score formula,

x = z * +

x = -1.13 * 5.05 + 155.69 = 149.98

x = 1.13 * 5.05 + 155.69 = 161.40

Two values are : 149.98 and 161.40

(c)

P(Z < 1.695) = 0.955

z = 1.695

Using z-score formula,

x = z * +

x = 1.695 * 5.05 + 155.69 = 164.25

score = 164.25