The scores on an achievement test are normally distributed w

The scores on an achievement test are normally distributed with a mean of 500 and the standard deviation of 100.

a. What is the probability that a score is between 450 and 650?

b. Find the exam score which has the property that 85% of all exam scores are higher than that score.

Solution

mu = 500

sigma = 100

a) P(450<x<650)

= P(-0.5<z<1.5)

= 0.1915+0.4332

= 0.6247

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b) 85th percentile z value = 1.04

x value = 500+100(1.04)

= 604