____ 4. Stephanie is self-employed. In 2019 she drove 1,000 miles for business out of a total 10,000 miles for the year. Her auto expenses for the year were: gasoline - $500; insurance - $1,000; repairs - $200; business parking - $400. How much is her automobile deduction if she uses the standard mileage method?

            a.         $580

            b.         $980

            c.         $2,680

            d.         $2,100

            e.         $210

            f.          $0.

____ 5. An aggressive young attorney is an employee of a small law firm that provides him with an adequate office. He uses the den in his home to prepare legal briefs and review legal documents related to his employment. Assuming the attorney lives near the firm's office and he always has easy access to the office, which of the following statements most accurately describes the deductibility of the home office expenses incurred by the attorney?

            a.         If the den is used exclusively for business purposes, the expenses are deductible.

            b.         If the den is used exclusively for business purposes on a regular basis, the expenses are deductible.

            c.         If the den is used exclusively for business purposes on a regular basis to work for and see clients, the expenses are deductible.

            d.         In this situation, the expenses are not deductible.

            e.         The home office deduction was completely eliminated as a result of the Tax Cuts and Jobs Act of 2017.

____ 6. T's employer provides an office for her in its downtown headquarters. Which of the following statements is true?

            a.         T maintains an office in her home that she uses to conduct work related to her rental property. Even though the rental activities may be considered a business, no deduction can be allowed because T's principal business is that of being an employee and its primary location is downtown.

            b.         T regularly meets with clients of her employer's business in her home office, which is exclusively used for such purpose. T is entitled to the home office deduction without further inquiry.

            c.         T maintains a home office that is exclusively used on a regular basis to conduct work regarding her investment portfolio. No deduction is allowed.

            d.         None of the statements above are true.

The research director at the Nie Pójdzie Motor Club was interested whether the annual miles driven by residents of Arkansas was greater than the 2019 average of 13,452 annual miles for a driver in the South Central region. A random sample of licensed Arkansan drivers was drawn, and a hypothesis test was performed using the .05 significance level. Some parts of the output are shown below. Please answer the following questions (a to g) using the output below. (3.5 pts.)

a) What are the degrees of freedom?

b) State the H₀ and H_a.

c) Identify the decision rule using the critical value of t (round to three decimal places).

d) Identify the decision rule using the p value method.

e) State the test statistic (t _calc)

f) What is the p value?

g) Do you reject or not reject H₀? Explain your decision using the output

The research director at the Nie Pójdzie Motor Club was interested whether the annual miles driven by residents of Arkansas was greater than the 2019 average of 13,452 annual miles for a driver in the South Central region. A random sample of licensed Arkansan drivers was drawn, and a hypothesis test was performed using the .05 significance level. Some parts of the output are shown below. Please answer the following questions (a to g) using the output below. (3.5 pts.)

a) What are the degrees of freedom?

b) State the H₀ and H_a.

c) Identify the decision rule using the critical value of t (round to three decimal places).

d) Identify the decision rule using the p value method.

e) State the test statistic (t _calc).

f) What is the p value?

g) Do you reject or not reject H₀? Explain your decision using the output.

Below is a list of gas mileage ratings for selected passenger cars in miles per gallon.

16.2 20.3 31.5 30.5 21.5 31.9 37.3 27.5 27.2 34.1 35.1 29.5 31.8 22.0 17.0 21.6

Find the mean, standard deviation, five - number summary, IQR, and identify any outliers. Use the five - number summary to sketch a boxplot. What does the boxplot tell you about the distribution of the data? (20 points)

The table below contains the overall miles per gallon​ (MPG) of a type of vehicle.

Construct a 95​% confidence interval estimate for the population mean MPG for this type of​ vehicle, assuming a normal distribution.The 95​% confidence interval estimate is from ____ MPG to ____ MPG.

​(Round to one decimal place as​ needed.)

Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and a standard deviation of 30.9 and 2.7 mpg, respectively. [You may find it useful to reference the z table.]

a. What is the probability that a randomly selected passenger car gets more than 32 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

b. What is the probability that the average mpg of four randomly selected passenger cars is more than 32 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

c. If four passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 32 mpg? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)

Gas Mileage. Based on tests of the Chevrolet Cobalt, engineers have found that the miles per gallon in highway driving are normally distributed, with a mean of 32 MPG and a standard deviation of 3.5 MPG.

a) What is the probability that a randomly selected Cobalt gets more than 34 MPG?

b) Suppose that 10 Cobalts are randomly selected and the MPG for each car are recorded. What is the probability that the mean MPG exceeds 34 MPG?

c) Suppose 20 Cobalts are randomly selected and the MPG for each car are recorded. What is the probability that the mean MPG exceeds 34 MPG?

Part A: Increasing Piston Displacement (L)

1. Calculate the product of the pressure P and length L for every row in both data tables.

2. Calculate the deviation for each value of PL.

Part B: Decreasing Piston Displacement (L)

A contractor is interested in the total cost of a project for which he intends to bid. He estimates that materials will cost P25000 and that his labour will cost P900 per day. The contractor then formulates the probability distribution for completion time (X), in days, as given in the following table. Completion time in days (X) 10 11 12 13 14 P(X=x) 0.1 0.3 0.3 0.2 0.1 a) Determine the total cost function C for the project. b) Find the mean and variance for completion time X. c) Find the mean, variance and standard deviation for the total cost C.