SOLUTION: A corporation�s fleet cars have an average annual operating cost of $100,000. Suppose the operating costs are normally distributed with a standard deviation of $8000. What is the

Question 1121957: A corporation�s fleet cars have an average annual operating cost of $100,000. Suppose the operating costs are normally distributed with a standard deviation of $8000.
What is the figure, in thousands of dollars, above which 10% of the operating costs will lie?
Give the answer to the nearest thousands of dollars and omit the $ sign in your answer (eg, if you think the answer is $100,000, enter 100 into the box).
Thanks very much
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
mean is 100,000
standard deviation is 8,000
you are looking for the operating costs that are greater than 90% of the operating costs.
they would be in the top 10%.
find the z-score where 90% of the area under the normal distribution curve is to the left of it.
that z-score will be 1.281551567 according to my TI-84 Plus calculator.
use the z-score formula to find the raw score associated with that.
the formula is z = (x - m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation.
that formula becomes:
1.281551567 = (x - 100,000) / 8,000.
solve for x to get x = 1.281551567 * 8,000 + 100,000 = 110,252.4125.
round that to the nearest thousand and provide it in thousands of dollars and the answer is 110.

to confirm, i used the following online calculator.

http://davidmlane.com/hyperstat/z_table.html

the calculator confirmed that 10% of the operating costs were above 110,252.4.

here's the what the calculator output looked like.

$$$

bottom line:

your answer should be 110.

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