# Normal distribution of incomes

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.