3) The average annual inflation rate in the United States over the past 98 years

Question

3) The average annual inflation rate in the United States over the past 98 years is 3.37% and has a standard deviation of approximately 5% (Inflationdata.com). În 1980, the inflation rate was above 13%. If the annual inflation rate is normally distributed, what is the probability that inflation will be above 13% next year? 4) Suppose residents in a well-to-do neighborhood pay an average overall tax rate of 25% with a standard deviation of 8%. Assume tax rates are normally distributed. What is the probability that the mean tax rate of 16 randomly selected residents is between 20% and 30%.

Explanation / Answer

Ans:

3)Mean=3.37 and standard deviation=5

z=(13-3.37)/5

z=1.926

P(z>1.926)=0.0271

4)Mean=25 and standard deviation=8

standard error of mean=8/sqrt(16)=2

z(20)=(20-25)/2=-2.5

z(30)=(30-25)/2=2.5

P(-2.5<z<2.5)=P(z<2.5)-P(z<-2.5)=0.9938-0.0062=0.9876

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