Exam 1: Stats Start Here

Owners of a minor league baseball team believe that a Normal model is useful in projecting the number of fans who will attend home games. They use a mean of 8500 fans and a standard deviation of 1500 fans. Draw and clearly label this model.

A company's manufacturing process uses 500 gallons of water at a time. A "scrubbing" machine then removes most of a chemical pollutant before pumping the water into a nearby lake. Legally the treated water should contain no more than 80 parts per million of the chemical, but the machine isn't perfect and it is costly to operate. Since there's a fine if the discharged water exceeds the legal maximum, the company sets the machine to attain an average of 75 ppm for the batches of water treated. They believe the machine's output can be described by a Normal model with standard deviation 4.2 ppm. (SHOW WORK.) a. What percent of the batches of water discharged exceed the 80ppm standard? b. The company's lawyers insist that they have not more than 2% of the water over the limit. To what mean value should the company set the scrubbing machine? Assume the standard deviation does not change. c. Because achieving a mean that low would raise the costs too much, they decide to leave the mean set at 75 ppm and try to reduce the standard deviation to achieve the "only 2% over" goal. Find the new standard deviation needed. d. Explain what achieving a smaller standard deviation means in this context.

To determine if people's preference in dogs had changed in the recent years, organizers of a local dog show asked people who attended the show to indicate which breed was their favorite. This information was compiled by dog breed and gender of the people who responded. The table summarizes the responses. Female Male Total Yorkshire Terrier 73 59 Dachshund 49 47 Golden Retriever 58 33 Labrador 37 41 Dalmatian 45 28 Other breeds 86 67 Total -Do you think the breed selection is independent of gender? Give statistical evidence to support your conclusion.

House calls A local plumber makes house calls. She charges $30 to come out to the house and $40 per hour for her services. For example, a 4-hour service call costs $30 + $40(4) =$190. a. The table shows summary statistics for the past month. Fill in the table to find out the cost of the service calls. Statistic Hours of Service Call Cost of Service Call Mean 4.5 Median 3.5 SD 1.2 IQR 2.0 Minimum 0.5 b. This past month, the time the plumber spent on one service call corresponded to a z-score of -1.50. What was the z-score for the cost of that service call?

A research company frequently monitors trends in the use of social media by American Adults. The results of one survey of 1846 randomly selected adults looked at social media use versus age group. The table summarizes the survey results. $\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Age Group }$ start text Uses Social Media end text 18-29 30-49 50-64 65+ Total Yes 328 417 288 114 No 67 125 265 242 Total -What is the marginal distribution of age groups?

Dimes minted in the United States average 2.286 g with a standard deviation of 0.06 g. A couple chemistry students were trying out their teacher's new scale by weighing a bunch of coins. The found a nickel that weighed 5.19 g and a dime that weighed 2.45 g. Which coin was more exceptionally heavy? Explain.

Suppose that the student taking 22 credit hours in the data set in the previous question was actually taking 28 credit hours instead of 22 (so we would replace the 22 in the data set with 28). Indicate whether changing the number of credit hours for that student would make each of the following summary statistics increase, decrease, or stay about the same: a. mean b. median c. range d. IQR e. standard deviation

One thousand students from a local university were sampled to gather information such as gender, high school GPA, college GPA, and total SAT scores. The results were used to create histograms displaying high school grade point averages (GPA's) for both males and females. Compare the grade distribution of males and females.

Which of the W's are unknown for these data?

Environmental researchers have collected rain acidity data for several decades. They want to see if there is any evidence that attempts to reduce industrial pollution have produced a trend toward less acidic rainfall. They should display their data in a(n)…

We collect these data from 50 male students. Which variable is categorical?

Which type of plot would be least likely to reveal that a distribution is bimodal?

Although most of us buy milk by the quart or gallon, farmers measure daily production in pounds. Guernsey cows average 39 pounds of milk a day with a standard deviation of 8 pounds. For Jerseys the mean daily production is 43 pounds with a standard deviation of 5 pounds. When being shown at a state fair a champion Guernsey and a champion Jersey each gave 54 pounds of milk. Which cow's milk production was more remarkable? Explain.

At a large business, employees must report to work at 7:30 A.M. The arrival times of employees can be described by a Normal model with mean of 7:22 A.M. and a standard deviation of four minutes. a. What percent of employees are late on a typical work day? b. A psychological study determined that the typical worker needs five minutes to adjust to their surroundings before beginning their duties. What percent of this business' employees arrive early enough to make this adjustment? c. Because late employees are a distraction and cost companies money, all employees need to be on time to work. If the mean arrival time of employees does not change, what standard deviation would the arrival times need to ensure virtually all employees are on time to work? d. Explain what achieving a smaller standard deviation means in the context of this problem.

In November 2003 Discover published an article on the colonies of ants. They reported some basic information about many species of ants and the results of some discoveries found by myrmecologist Walter Tschinkel of the University of Florida. Information included the scientific name of the ant species, the geographic location, the depth of the nest (in feet), the number of chambers in the nest, and the number of ants in the colony. The article documented how new ant colonies begin, the ant-nest design, and how nests differ in shape, number, size of chambers, and how they are connected, depending on the species. It reported that nest designs include vertical, horizontal, or inclined tunnels for movement and transport of food and ants. -Describe the W's, if the information is given: · Who: · What: · When: · Where: · How: · Why:

A survey conducted in a college intro stats class asked students about the number of credit hours they were taking that quarter. The number of credit hours for a random sample of 16 students is given in the table. 10 10 12 14 15 15 15 15 17 17 19 20 20 20 20 22 a. Sketch a histogram of these data. b. Find the mean and standard deviation for the number of credit hours. c. Find the median and IQR for the number of credit hours. d. Is it more appropriate to use the mean and standard deviation or the median and IQR to summarize these data? Explain.

The mean number of hours worked for the 30 males was 6, and for the 20 females was 9. The overall mean number of hours worked…

The Wechsler Adult Intelligence Scale - Revised (WAIS-R) follow a Normal model with mean 100 and standard deviation 15. Draw and clearly label this model.

Adult female Dalmatians weigh an average of 50 pounds with a standard deviation of 3.3 pounds. Adult female Boxers weigh an average of 57.5 pounds with a standard deviation of 1.7 pounds. One statistics teacher owns an underweight Dalmatian and an underweight Boxer. The Dalmatian weighs 45 pounds, and the Boxer weighs 52 pounds. Which dog is more underweight? Explain.

To see if your school's ACT scores are improving since implementing a new program, the ACT Scores for the past several years should be displayed in a