Problems 15 and 16 pertain to the following situation. Annual starting salaries

Question

Problems 15 and 16 pertain to the following situation.

Annual starting salaries in a certain region of the U. S. for college graduates with an engineering major are normally distributed with mean $39725 and standard deviation $7320.

The probability that a randomly selected graduate with an engineering major has a starting salary of at least $39000 is about

(a) .10 (b) .54 (c) .90 (d) .73 (e) .46

Suppose a school takes a sample of 125 such graduates and records the annual starting salary of each. The probability that the sample mean would be at least $39000 is about

(a) .87 (b) .46 (c) 1.00 (d) 0.00 (e) .54

Explanation / Answer

1. P(X > 39000)

= P(z > (39000 - 39725)/7320)

= P(z > -0.1)

= 0.54

Option b is correct.

2. P(X > 39000)

= P(z > (39000 - 39725)/(7320/sqrt(125))

= P(z > -1.11)

= 0.87

Option a is correct.

Option b is correct.

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