As part of an application process, each candidate must pass an entrance paper. T

Question

As part of an application process, each candidate must pass an entrance paper. The candidate scores on the entrance paper follow a normal distribution with a mean of 60 points and a standard deviation of 12 points. If a candidate is a top performer, scores more than 75 points on the entrance paper, they are automatically asked for a phone interview. However, if a candidates scores in the top 30% of the distribution, the candidate is invited to take the entrance paper again within two weeks of the original paper date, otherwise the candidate must wait at least 1 year before attempting the paper again.

1) What is the minimum score that a candidate in the top 30% of the distribution can get in order to be invited to take the entrance paper again?

a) 72 points

b) 53.76 points

c) 66.24 points

d) 84 points

2) What proportion of candidates are automatically asked for a phone interview?

a) 0.16

b) 0.68

c) 0.1056

d) 0.8944

e) 0.84

Explanation / Answer

1). b) 53.76 points

Using, Y = { 1/[ * sqrt(2) ] } * e-(x - )2/22

where X is a normal random variable, is the mean, is the standard deviation, is approximately 3.14159, and e is approximately 2.71828.

2). c) 0.1056

Since = 60 and = 12 we have:

P ( X > 75 ) = P ( X > 7560) = P ( X/ > 7560/12)

Since Z = x/ and 7560/12 = 1.25 we have:

P ( X > 75 ) = P ( Z > 1.25 )

Using the standard normal table to conclude that:

P (Z > 1.25) = 0.1056

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