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?

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?


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a(1500) = (1500-1280)/420 = 220/420 = 0.5238
P(x > 1500) = P(z > 0.5238) = 0.30 = 30%
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b. What fraction of the employees cost between $1,500 and $2,000 per year?
z(2000) = (2000-1280)/420 = 1.7143...
P(1500 < x < 2000) = P(0.5238 < z < 1.7143) = 0.257
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c. Estimate the percent that did not have any dental expense.
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z(0) = (0-1500)/420 = -3.5714..
P(x < 0) = P(z < -3.4714) = 0.0002589..
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d. What was the cost for the 10 percent of employees who incurred the highest dental expense?
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invNorm(0.90) = z = 1.2816
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x = zs+u
x = 1.2816*420+1280
x = $1818.25
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Cheers,

 

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