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According to the Internal Revenue Service, the average length of time for an individual to complete (keep records for, learn, prepare, copy, assemble, and send) IRS Form 1040is 10.53hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36taxpayers.

a. In words, Χ=_____________

b. In words,X=_____________

c. X¯~_____(_____,_____)

d. Would you be surprised if the 36taxpayers finished their Form 1040s in an average of more than 12hours? Explain why or why not in complete sentences.

e. Would you be surprised if one taxpayer finished his or her Form 1040in more than 12hours? In a complete sentence, explain why.

Short Answer

Expert verified

a. length of time for an individual to complete IRS

b. mean length of time for a sample of 36taxpayers to complete the IRS form

c. X~N10.53,13

d. Yes. I would be surprised because the probability is almost0

e. No. I would not be totally surprised because the probability is0.2312

Step by step solution

01

Given information

the average length of time for an individual to complete (keep records for,

learn, prepare, copy, assemble, and send) IRS Form1040 is 10.53hours (without any attached schedules).

The distribution is unknown.

Let us assume that the standard deviation is two hours.

02

Explanation (part a)

The definition of random variable is given by,

X=length of time for an individual to complete IRS form 1040, in hours.

03

Explanation (part b)

In other words, the sample random variable is defined as, X=the mean length of time for a sample of 36taxpayers to complete IRS form.

04

Explanation (part c)

The random variable can be expressed as,X~N10.53,13normal distribution.

05

Explanation (part d)

On taking normal CDF, we get the probability is0

Yes. I would be surprised because the probability is almost0

06

Explanation (part e)

If one taxpayer finished his or her Form in more than twelve hours, the probability is about0.2312

No. I would not be totally surprised because the probability is 0.2312

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