Question

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 1040 is 10.18 hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36 taxpayers. Part (a) In words, define the random variable X. the number of taxpayers sampled the length of time, in minutes, for an individual to complete IRS Form 1040 the number of individuals who complete IRS Form 1040 the length of time, in hours, for an individual to complete IRS Form 1040 Part (b) In words, define the random variable X. the average length of time, in hours, for a sample of 100 taxpayers to complete IRS Form 1040 the average income of a random sample of taxpayers the average length of time, in hours, for a sample of 36 taxpayers to complete IRS Form 1040 the average length of time, in minutes, for a sample of 36 taxpayers to complete IRS Form 1040 Part (c) Give the distribution of X. (Round your answers to two decimal places.) X ~ , Part (d) Find the probability that the 36 taxpayers took an average of more than 12 hours to finish their Form 1040s. (Round your answer to four decimal places.) Part (e) Would you be surprised if the 36 taxpayers finished their Form 1040s in an average of more than 12 hours? Explain why or why not in a complete sentence. No, because the probability is very close to 1. Yes, because the probability is very close to 0.

Answer 1

a) The length of time, in hours, for an individual to complete IRS Form 1040.

b) in minutes, for a sample of 36 taxpayers to complete IRS Form 1040 the average length of time.

c) $\mu_{\bar x}$ = 10.18

  $\sigma_{\bar x} = \sigma/\sqrt n$

= 2/$\sqrt {36}$

= 0.33

$\bar x$ ~ N(10.18, 0.33)

d) P($\bar x$ > 12)

= P(($\bar x$ - $\mu$ )/($\sigma/\sqrt n$) > (12 -  $\mu$)/($\sigma/\sqrt n$))

= P(Z > (12 - 10.18)/0.33)

= P(Z > 5.52)

= 1 - P(Z < 5.52)

= 1 - 1 = 0

e) Yes, because the probability is very close to 0.