Find the probability income

Question

The per capita disposable income for residents of a U.S. city in a recent year is normally distributed, with a mean of approximately $44,000 and a standard deviation of about $2450. Use this information to complete the following.

5. Find the probability that the disposable income of a resident is more than $45,000. Is this an unusual event? Explain.

6. Out of 800 residents, about how many would you expect to have a disposable income between $40,000 and $42,000?

7. Between what two values does the middle 60% of disposable incomes lie?

Answer 1

p (X> 45000)

On a TI-84

normalcdf

lower = 45000

upper = 1E99

mean = 44000

sd = 2450

p = 0.3416

p = 0.3416 = 34% so relatively high probability (if p< 0.05 would be unusual)

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Find p ( 40000 < x < 42000)

normalcdf

lower = 40000

upper = 42000

mean = 45000

sd = 2450

multiply the probability by 800, and round to the nearest integer

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we want to find y so that p ( 45000 - y < X < 45000 + y) = 0.60

By symmetry this means p ( X < 45000-y) = 0.20

invnorm

area = 0.20

mean = 45000

sd = 2450

giving 42938

This will be 45000 - y, giving y = 2062

so upper bound = 45000 + 2062 = 47062

So two values are 42938, 47062