Question

# The test scores for the analytical writing section of the Graduate Record Examination can be approximated...

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%

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

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