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Please solve the following problem:

Scores on an examination are assumes to be normally distributed with mean 78 and variance 36.

a.What is the probability that a person taking the examination scores higher than 72?

b.Suppose that students scoring in the top 10% of this distribution are to receive an A grade. What is the minimum score a student must achieve to earn an A grade?

c.What must be the cutoff point for passing the examination if the examiner wants only the top 28.1% of all scores to be passing?

d.Approximately what proportion of students have scores 5 or more points above the score that cuts off the lowest 25%?

e.If it is known that a student's score exceeds 72, what is the probability that his or her score exceeds 84?

(Please see the attached document)

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Solution Preview

m = 78, s = sqrt 36 = 6; z = (x - m)/s

(a) z = (72 - 78)/6 = -1

P(x > 72) = P(z > -1) = 0.8413

(b) Area under the standard normal curve is 0.10 for z = 1.2816

The ...

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