Essay Assignment
1. A sample of retailers reported that they had the following number of copies of statistics textbooks in inventory: 57, 81, 69, 84, 85, 79, 71, 74, 55.
a. What is the mean number of textbooks in inventory?
b. What is the median number of textbooks in inventory?
c. What is the range of the number of textbooks in inventory?
d. What is the standard deviation of the number of textbooks in inventory?
2. IRS data show that 15% of personal tax returns reporting an adjusted gross income (AGI) of more than $2,000,000 will be subject to a computer audit. This year a CPA completed 16 returns with an AGI of more than $2,000,000. The CPA wants to know the likelihood that the returns will be audited.
a. What probability distribution applies to this situation?
b. What is the probability exactly one of these returns is audited?
c. What is the probability at least one of these returns is audited?
3. For certain personal tax returns, the IRS will compute the amount to refund a taxpayer. Suppose the Chicago office of the IRS processes an average of three returns per hour that require a refund calculation.
a. What probability distribution applies to this situation?
b. What is the probability that the IRS processes exactly three refunds in a particular hour that requires a refund calculation?
c. What is the probability the IRS does not compute a refund on any return in an hour?
d. What is the probability the IRS processes at least one return in a particular hour that requires a refund calculation?
4. A CPA studied the number of exemptions claimed on tax returns. The data are summarized as follows:
|
Exemptions
|
Percent
|
|
1
|
10
|
|
2
|
20
|
|
3
|
50
|
|
4
|
20
|
a. What is the mean number of exemptions claimed?
b. What is the variance of the number of exemptions claimed?
c. What is the standard deviation of the number of exemptions claimed?
5. The IRS reports that the mean refund for a particular group of taxpayers was $1,600. The distribution of tax refunds follows a normal distribution with a standard deviation of $850.
a. What percentage of the refunds are between $1,600 and $2,000?
b. What percentage of the refunds are between $900 and $2,000?
c. What percentage of the refund are between $1,800 and $2,000?
d. Ninety-five percent of the refunds are for less than what amount?
Format your assignment according to the following formatting requirements:
1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also includes a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
3. Also include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.