Dr Jones works at a large state university where graduate st

Dr. Jones works at a large state university where graduate students are paid by the hour. He has been put in charge of auditing the graduate pay across departments. He knows that the hourly wage paid to graduate personnel is approximately normally distributed with a mean ? = $12.00 and a standard deviation of ? = $2.50.

1. Jillian earns $13.25 per hour. What percentage of employees does she earn more than (that is, what is her percentile rank for income) at the university?

2.What salary range accounts for the middle 50% of graduate students?

Solution

(1) P(X<13.25) = P((X-mean)/s <(13.25-12)/2.5)

=P(Z<0.5) =0.6915 (from standard normal table)

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(2) Given a=1-0.5=0.5, Z(0.5/2) = Z(0.25) =0.67 (from standard normal table)

So the lower bound is

mean - Z*s = 12-0.67*2.5 =10.325

So the upper bound is

mean+ Z*s =12+0.67*2.5 =13.675