# Continuous probability distribution - Dental insurance for employees

Shaver Manufacturing, 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 distribution, with a mean of $1280 and a standard deviation of $420.

What fraction of the employees cost more than $1500 per year for dental expenses?

What fraction of the employees cost between $1500 and $2000 per year?

Estimate the percent that did not have any dental expense.

What was the cost for the 10 percent of employees that incurred the highest dental expense?

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#### Solution Preview

Solution

2.

We are given that annual cost has a normal distribution N (1280, 420). The fraction of employees cost more than $ 1500 per year is given by

P [x >1500] = 1- P[x ≤ 1500]

= 1- P [ ]

= 1-p [ z ≤ .52 ]

=

= .3015 using table of N(0,1)

= .30 or 30%

→ 30% of The employees me cost more ...

#### Solution Summary

Using equations and calculations, this solution determines the percentage of employees in each group in relation to dental expenses, as well as the highest dental expense.