9 According to a website about salaries the national average

9. According to a website about salaries, the national average salary as of October 2003 for a human resources clerk was $29,932. We assume that the annual salaries for clerks are normally distributed with a standard deviation of $1,890. (Give your answers correct to two decimal places.) (a) Find the percentage who earn less than $26,780. % (b) Find the percentage who earn more than $32,284.

Solution

(a) Find the percentage who earn less than $26,780. %

P(X<26,780) = P((X-mean)/s <(26780-29932)/1815)

=P(Z<-1.74) = 0.0409 (from standard normal table)

i.e. 4.09%

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(b) Find the percentage who earn more than $31,948. %

P(X>31948) = P(Z>(31948-29932)/1815)

=P(Z>1.11) =0.1335 (from standard normal table)