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) P(X>2000)

= P(Z>(2000-2913)/950)

= P(Z>-0.96)

Use excel function

1-NORMSDIST(-0.96)

= 0.8317

b) P(1600<X<2500)

= P((1600-2913)/950<Z<(2500-2913)/950)

= P(-1.38<Z<-0.43)

c) For 35th Percentile = NORMSINV(0.35)*950+2913

= 2546.95

Use excel function

NORMSDIST(-1.38)-NORMSDIST(-0.43)

= 0.2484

c) P(3200<X<4000)

= P((3200-2913)/950<Z<(4000-2913)/950)

= P(0.30<Z<1.14)

Use excel function

NORMSDIST(1.14)-NORMSDIST(0.30)

= 0.2550

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.