According to the National Association of Colleges and Employers, the average starting salary for new college graduates in health sciences is $51,541. The average starting salary for new college graduates in business is $53,901 (National Association of Colleges and Employers website, January 2015). Assume that starting salaries are normally distributed and that the standard deviation for starting salaries for new college graduates in health sciences is $11,000. Assume that the standard deviation for starting salaries for new college graduates in business is $15,000.
a. What is the probability that a new college graduate in business will earn a starting salary of at least $65,000?
b. What is the probability that a new college graduate in health sciences will earn a starting salary of at least $65,000?
c. What is the probability that a new college graduate in health sciences will earn a starting salary of less than $40,000?
d. How much would a new college graduate in business have to earn in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences?

Question

05-03-2020
Mathematics

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According to the National Association of Colleges and Employers, the average starting salary for new college graduates in health sciences is $51,541. The average starting salary for new college graduates in business is $53,901 (National Association of Colleges and Employers website, January 2015). Assume that starting salaries are normally distributed and that the standard deviation for starting salaries for new college graduates in health sciences is $11,000. Assume that the standard deviation for starting salaries for new college graduates in business is $15,000.
a. What is the probability that a new college graduate in business will earn a starting salary of at least $65,000?
b. What is the probability that a new college graduate in health sciences will earn a starting salary of at least $65,000?
c. What is the probability that a new college graduate in health sciences will earn a starting salary of less than $40,000?
d. How much would a new college graduate in business have to earn in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences?

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farisfekeri farisfekeri · Answer 1 · 2020-03-06T02:40:19+01:00

Answer:

Part (a) : 0.2297

Part (b) : 0.1112

Part (c) : 0.1469

Part (d) : 77,171

Step-by-step explanation:

Given info on Health Sciences:

Mean = $51,541

Standard Deviation = $11,000

Given info on Business:

Mean = $53,901

Standard Deviation = $15,000

Part (a)

Let X represents the new college graduate in business,

P (X ≥ 65,000) = 1 - P (X < 65,000)

= 1 - P ( z < [tex]\frac{65,000 - 53,901}{15,000}[/tex] )

= 1 - P ( z < 0.74)

= 1 - 0.77035

= 0.2297

Part (b)

Let Y represents the new college graduate in Health Sciences,

P (Y ≥ 65,000) = 1 - P (Y < 65,000)

= 1 - P ( z < [tex]\frac{65,000 - 51,541}{11,000}[/tex] )

= 1 - P ( z < 1.22)

= 1 - 0.88877

= 0.1112

Part (c)

Let Y represents the new college graduate in Health Sciences,

P (Y < 40,000) = P (Y < [tex]\frac{40,000-51,541}{11,000}[/tex])

= P ( z < -1.05 )

= 0.1469

Part (d)

To have a starting salary higher than 99%, the z-score = 2.33. Let A represents the salary of a new college graduate in health sciences higher than 99% of all starting salaries.

[tex]2.33 = \frac{A - 51,541}{11,000}[/tex]

[tex]A = 77,171[/tex]

77,171 new college graduate in business have to earn in order to have a starting salary higher than 99% of all starting salaries of new college graduates in health sciences.