Question

**PLEASE READ QUESTION CAREFULLY thank you!** The average salary for graduates entering the actuarial field is $40,000. If the salaries are normally distributed with a variance of $25,000, find the probability that a group of nine graduates will have a group average over $45000. a) complete z curve sketch b) calculate z formula c) determine probability

Answer 1

Given: = 40000, = 25000 and = 5000, n = 9

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(a)

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(b) The z score is given by

For n = 9, P(X > 45000), we need to first find P(X < 45000) as the tables gives probabilities to the left.

z = (45000 - 40000) / [5000 / (sqrt(9)] = 3
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(c) The Probability calculation:

At z = 12, P(X < 45000) = 0.9987

Therefore P(X > 45,000) = 1 - 0.9987 = 0.0013

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