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?
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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
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