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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.

\$2.49