Question 201577: Shaver Manufacturing, Inc. offers dental insurance to its employees. A recent study by the human resource director shows the annual cost per employee per year followed the normal probability distribution, with a mean of $1,280 and a standard deviation of $420 per year.
a. What fraction of the employees cost more than $1,500 per year for dental expenses?
b. What fraction of the employees cost between $1,500 and $2,000 per year?
c. Estimate the percent that did not have any dental expense.
d. What was the cost for the 10 percent of employees who incurred the highest dental expense?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! to answer this question, it helps to have a statistical calculator.
if not then statistical tables would help.
the normal distribution curve has the mean at the halfway point with equal distributions above and below this.
roughly 68% of the population has scores within plus or minus 1 standard deviation.
roughly 95% of the population has scores within plus or minus 2 standard deviations.
roughly 99.7% of the population has scores within plus or minus 3 standard deviations.
to answer your question, I looked up an online statistical calculator at the following internet address.
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http://davidmlane.com/hyperstat/z_table.html
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you can copy and paste that internet address in your internet address bar to see what's happening.
there are 2 graphs.
the top graph allows you to enter mean and standard deviation.
the bottom graph allows you to enter percent of shaded area.
your first question:
what fraction of the employees cost more than $1500 per year?
the answer was roughly 30% (.300206).
if you look at the top graph you'll see that is the area of the curve to the right of 1500. you would enter 1500 in the above slot and select it (after you entered 1280 as the mean and 420 as the standard deviation).
your second question:
What fraction of the employees cost between $1,500 and $2,000 per year?
the answer was roughly 25.7% (.256967).
if you look at the graph you'll see that is the area of the curve between 1500 and 2000. you would enter 1500 and 2000 in the between slot of the top graph and select it (mean of 1280 and standard deviation should still be entered).
your third question:
Estimate the percent that did not have any dental expense.
the answer to that is roughly .1% (.001153).
you enter 0 in the below slot of the top graph and select it.
your fourth question:
What was the cost for the 10 percent of employees who incurred the highest dental expense?
the answer to that is somewhere in the neighborhood of 1818 (1818.2516).
you use the bottom graph for this to make it easier. mean is 1280, standard deviation is 420. enter .10 in the shaded area slot and then select above.
this tells you that 10% of the employees had expenses equal to 1818 or greater.
review your normal distribution curve and you should be able to see how this was done and why.
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