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

____________________________________

(a)

____________________________________

(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

_______________________________________

(c) The Probability calculation:

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

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

______________________

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

28. 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 $45,000.
SHOW ALL WORK
Part A: Complete Z curve sketch: 3 pts
Part B: Calculate Z formula: 3 pts
Part C: Determine probability: 3 pts

The average salary for graduates entering the actuarial field is
$40,000. If the salaries are normally distributed with a standard
deviation of $25,000, find the probability that a) An individual
graduate will have a salary over $45,000. b) A group of nine
graduates will have a group average over $45000.

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While the average starting salary for graduates with an MBA
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