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    Continuous probability distribution - Dental insurance for employees

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    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

    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.