1 (a). The following data set lists a series of ACT scores {8, 12, 15, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 23, 23, 24, 25, 36}. Write down the five number summary and construct a boxplot which includes the position of the upper and lower fences

(b). At a tennis tournament a statistician keeps track of every serve. The statistician reported that the mean serve speed of a particular player was 104 miles per hour (mph) and the standard deviation of the serve speeds was 8 mph. Assume that the statistician also gave us the information that the distribution of the serve speed was bell shaped. What proportion of the player’s serves are expected to be between 112 mph and 120mph?

Floor Area Ratio (FAR)

You have purchased the land and lifts of an older ski resort. You are upgrading the lifts and are master planning the real estate development of the ski resort. After studying other resorts you come up with the following (back of the envelope) regression for the sales price per square foot of residential real estate in similar resorts:

P = 300 – 100d – 20F

Where d is distance in miles to the lifts and F is FAR. You ascertain that construction costs will be 140 per square foot regardless of FAR.

Given:

FAR Optimal Density Equation –

F = 160-100(3.587 ^e-8) / 20

Question:

With the Given Information and the Optimal Density Equation, what is the Optimal Point to extend development of the Ski Resort?

A federal watchdog is investigating an advertising claim that a certain device reduces gasoline consumption in cars. Seven devices have been tested and installed in cars belonging to the institution. To compare performance under standard conditions, the miles each car travels with a gallon of gasoline are measured in both situations, before and after installation.

Would you say that the federal monitoring body has conclusively proven that the device has no effect on the performance of cars?

Formulate the appropriate null hypothesis and alternative, with a α = 0.025. Your work should have detailed procedure and appropriate analysis.

In a test of braking performance, a tire manufacturer measured the stopping distance for one of its tire models. On a test track, a car made repeated stops from 60 miles per hour. The test was run on both dry and wet pavement, with results as shown below.

Wet   Dry
210   154
191   153
214   143
200   137
202   130
196   146
198   132
179   144
194   142
217   127

a) Construct a 95% confidence interval for the mean dry pavement stopping distance.

The confidence interval is?

(Round to one decimal place as needed.)

b) Construct a 95% confidence interval for the mean increase in stopping distance on wet pavement.

The confidence interval is?

(Round to one decimal place as needed.)

The wind speed in Laramie, Wyoming is normally distributed. The average wind speed for the state of Wyoming is approximately 20 mph. A curious student wanted to find out if the wind speed in Laramie was different than the state average. They took a sample of 25 random days in Laramie, measured the wind speed, and found an average of 18 mph with a standard deviation of 7.8 miles per hour.

Test the claim that the average wind speed in Laramie is less than the state average. Provide all six steps to the hypothesis test, using both a critical value AND a p-value to make your decision about the null.

Provide the confidence interval estimate of the true wind speed in Laramie.

Explain how your hypothesis test in 8_1 and your confidence interval in 8_2 are consistent.

In its Fuel Economy Guide for 2016 model vehicles, the Environmental Protection Agency provides data on 11701170 vehicles. There are a number of high outliers, mainly hybrid gas‑electric vehicles. If we ignore the vehicles identified as outliers, however, the combined city and highway gas mileage of the other 11461146 vehicles is approximately Normal with mean 23.023.0 miles per gallon (mpg) and standard deviation 4.94.9 mpg.

The quartiles of any distribution are the values with cumulative proportions 0.250.25 and 0.75.0.75. They span the middle half of the distribution.

What is the first quartile of the distribution of gas mileage? Use Table A and give your answer rounded to two decimal places.

?1=Q1=

mpg

What is the third quartile of the distribution of gas mileage? Use Table A and give your answer rounded to two decimal places.

?3=

1. Ross White’s machine shop uses 2,500 brackets during the course of a year, and this usage is relatively constant throughout the year. These brackets are purchased from a supplier 100 miles away for $15 each, and the lead time is 2 days. The holding cost per bracket per year is $1.50 (or 10% of the unit cost), and the ordering cost per order is $18.75. There are 250 working days per year.

   1. What is the EOQ?

   2. Given the EOQ, what is the average inventory? What is the annual inventory holding cost?

   3. In minimizing cost, how many orders would be placed each year? What would be the annual ordering cost?

   4. Given the EOQ, what is the total annual inventory cost (including purchase cost)?

   5. What is the time between orders?

   6. What is the ROP?

3.36

On March 11, 2011, a massive earthquake and tsunami triggered a major disaster at Japan’s

Fukushima nuclear plant. A plume extending to the northwest of the site deposited significant amounts of iodine-131, cesium-134, and cesium-137 up to 30 miles away. Iodine-131 has an 8-day half-life and cesium-137 has a 3-year half-life. Determine how long it will take 99% of the iodine-131 and 99% of the cesium-

137 to naturally decay (you can learn about “U.S. Nuclear Power Safety One Year after Fukushima” by readin

g the report written by D. Lochbaum and E. Lyman, located on the web site of the Union of Concerned Scientists, http://www.ucsusa.org/publications/publications-nuclear-power.html)

Margaret started her own business in the current year and will report a profit for her first year. Her results of operations are as follows:

Complete the table below to determine the net income Margaret should show on her Schedule C.

If an amount is zero, enter "0". If required, round the amounts to the nearest dollar.