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Answer:
a) The probability that a new college graduate in business will earn a starting salary of at least $65,000 is P=0.22965 or 23%.
b) The probability that a new college graduate in health sciences will earn a starting salary of at least $65,000 is P=0.11123 or 11%.
c) The probability that a new college graduate in health sciences will earn a starting salary of less than $40,000 is P=0.14686 or 15%.
d) A new college graduate in business have to earn at least $77,133 in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences.
Step-by-step explanation:
<em>a. What is the probability that a new college graduate in business will earn a starting salary of at least $65,000?</em>
For college graduates in business, the salary distributes normally with mean salary of $53,901 and standard deviation of $15,000.
To calculate the probability of earning at least $65,000, we can calculate the z-value:
The probability is then
The probability that a new college graduate in business will earn a starting salary of at least $65,000 is P=0.22965 or 23%.
<em>b. What is the probability that a new college graduate in health sciences will earn a starting salary of at least $65,000?</em>
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For college graduates in health sciences, the salary distributes normally with mean salary of $51,541 and standard deviation of $11,000.
To calculate the probability of earning at least $65,000, we can calculate the z-value:
The probability is then
The probability that a new college graduate in health sciences will earn a starting salary of at least $65,000 is P=0.11123 or 11%.
<em>c. What is the probability that a new college graduate in health sciences will earn a starting salary less than $40,000?</em>
To calculate the probability of earning less than $40,000, we can calculate the z-value:
The probability is then
The probability that a new college graduate in health sciences will earn a starting salary of less than $40,000 is P=0.14686 or 15%.
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<em>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?</em>
The z-value for the 1% higher salaries (P>0.99) is z=2.3265.
The cut-off salary for this z-value can be calculated as:
A new college graduate in business have to earn at least $77,133 in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences.
down 3 unit mean -3 outside root
right 2 unit mean -2 inside root,
so the answer is