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    Normal distribution of incomes

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    The monthly income of residents of Dayton is normally distributed with a mean of $3000 and a standard deviation of $500.

    Define the random variable in words.
    The mayor of Dayton makes $2,250 a month. What percentage of Dayton residents has incomes that are more than the mayor's?
    Individuals with incomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes?
    What are the minimum and the maximum incomes of the middle 95% of the residents?
    Two hundred residents have incomes of at least $4,440 per month. What is the population of Dayton?

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    The monthly income of residents of Dayton is normally distributed with a mean of $3000 and a standard deviation of $500. The mayor of Dayton makes $2,250 a month. What percentage of Dayton residents has incomes that are more than the mayor's?
    Solution:

    Mean = 3000, standard deviation = 500

    P(x > 2250) = P(z > -1.5) = 1 - P(z < -1.5) = 1 - 0.0668072 = 0.9331928

    93.32% of ...

    Solution Summary

    This solution answers various questions relating to a normal distribution of incomes.

    $2.19

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