Question 61523: Please help. I am having a hard time figuring this out. The book is Statstics for Management & Economics Abbreviates 7th Edition.
The recent average starting salary for new college graduates in computer information systems is $47,500. Assume salaries are normally distributed with a standard deviation of $4,500.
a) What is the probability of a new graduate receiving a salary between $45,000 and $50,000?
b) What is the probability of a new graduate getting a starting salary in excess of $55,000?
c) What percent of starting salaries is no more than $42,250?
d) What is the cutoff for the bottom 5% of the salaries?
e) What is the cutoff for the top 3% of the salaries?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The recent average starting salary for new college graduates in computer information systems is $47,500. Assume salaries are normally distributed with a standard deviation of $4,500.
a) What is the probability of a new graduate receiving a salary between $45,000 and $50,000?
P(45000
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b) What is the probability of a new graduate getting a starting salary in excess of $55,000?
P(x>55000)= P(z>([55000-47500]/4500)=0.04779...
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c) What percent of starting salaries is no more than $42,250?
P(X<=42,250) = P(z <= ([42250-47500]/4500) = 0.12167...
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d) What is the cutoff for the bottom 5% of the salaries?
The z-value associated with the bottom 5% is -1.64485
Using the formula z=(X-mu)/sigma you get:
4500(-1.64485)=X-47500
X= $40,098.16
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e) What is the cutoff for the top 3% of the salaries?
The z-value associated with the top 3% is 1.88079...
Using the same formula
4500(1.88079...)=X-47500
X=$55963.57
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Cheers,
Stan H.
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