Suppose there were a reason to believe that incomes in some population were norm

Question

Suppose there were a reason to believe that incomes in some population were normally distributed, with a mean of $49,000 per year, and a standard deviation of $4,500 per year.

a. What fraction of the population would make between $40,000 and $55,000 per year?

b. What fraction of the population would be described as below the poverty level, if that number is $24,250 (assuming a single wage-earner supporting a family of 4)?

c. If used blindly, this distribution would suggest that some people earn negative income per year. What fraction would that be?

Explanation / Answer

a)

P( 40000 - 49000 / 4500 < z < 55000-49000 / 4500)

P( -2 < z < 1.33) = 1 - 0.0228 - 0.0918 = 0.8854

b)

P( z < 24250 - 49000 / 4500 )

P( z < -5.5 ) = 0.000005

c. If used blindly, this distribution would suggest that some people earn negative income per year. What fraction would that be?

P( z < -49000 / 4500 )

P( z < 10.888 ) = 0.00000

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