According to the Internal Revenue Service, the average income tax refund for the

Question

According to the Internal Revenue Service, the average income tax refund for the 2011 tax year was $2,913. As- sume the refund per person follows the normal probability distribution with a standard deviation of $950. 11 a. What is the probability that a randomly selected tax return refund from the 2011 tax year will be 1. more than $2,000? 2. between $1,600 and $2,500? 3. between $3,200 and $4,000? 79 Continuous Proba b. Confirm the answers to part a using Excel or PHStat. c. What refund amount represents the 35th percentile of tax returns?

Explanation / Answer

a)

1)

2)

3)

b)

above results can be confirmed by excel formula: norm.dist(x,mean,std deviation,true)

for part 1) formula is =1-norm.dist(2000,2913,950,true) =0.8317

for part 2) formula is =norm.dist(2500,2913,950,true)-norm.dist(1600,2913,950,true) =0.2484

for part 3) formula is =norm.dist(4000,2913,950,true)-norm.dist(3200,2913,950,true) =0.2550

c)

for 35th percentile ; zscore =-0.3853

hence corresponding refund amount =mean+z*std deviation =2913-0.3853*950 =$2546.95

for normal distribution z score =(X-)/

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