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In: Statistics and Probability

the internal revenue service reports that the mean federal income tax paid in a recent year...

the internal revenue service reports that the mean federal income tax paid in a recent year was $8040. Assume that the standard deviation is $5000. The irs plans to draw a sample of 1000 tax returns to study the effect of a new law.

A) what is the probability that the sample mean tax is less than $8000?
B) what is the probability that the sample mean tax is between $7600 & $7900?
C) Find the 40th percentile of the sample mean
D) would it be unusual if the sample mean were less than $7500
E) can you tell whether it would be unusual for an individual to pay tax of less than $7500? Explain?

Solutions

Expert Solution

Let denotes the sample mean of federal income tax paid for a a sample of 1000 tax returns.

or

a) The probability that the sample mean tax is less than $8000

b) The probability that the sample mean tax is between $7600 & $7900

c) To find 40th percentile of the sample mean

d) The probability that the sample mean tax is less than $7500

e) Since is quite low, so it will be unusual for an individual to pay tax of less than $7500.

orchestra answered 2 years ago
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