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Frequency Distribution Table, Stem & Leaf, Histogram and Z-Score

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[Please see attachment for data and charts]

1. Identify each number as either continuous or discrete.

a. The average speed of cars passing a speed trap on the Maine Turnpike between 3 PM and 6 PM on a given Monday.
b. A census taker wants to know the number of Maine families with preteens.
c. The temperature of the ocean at various depths.

2. For each of the following variables, indicate whether it is qualitative or quantitative.

a. The admitting diagnosis of patients admitted to a mental health clinic.
b. The weights of babies born in a hospital during a year.
c. The class rank of high school seniors at the local high school.
d. The religion of the sample subjects.

3. Identify each study as either experimental or observational.

a. A sample of fish is taken from the Androscoggin River, in Maine, to measure the level of mercury in the fish.
b. A research scientist gives a weight loss drug to a group of 500 patients and a placebo to another 500 patients to determine if the weight loss drug has an effect on the patients.

4. In response to a poll on a Dateline NBC program about wildlife conservation, 1276 of 1450 callers said they would be willing to spend more money on imported fossil fuels in order to eliminate the possibility of oil drilling in national parks set aside as wildlife preserves. NBC followed with the announcement that 88% of Americans are willing to spend money to protect wildlife preserves. Do you think that the group of people who responded is likely to be representative of all Americans? Explain your answer.

5. Construct a frequency table with 4 classes for the following data on the charge for monthly long distance phone bills for the last year: $17.06, $20.96, $25.97, $26.41, $22.02, $27.34, $18.67, $24.88, $24.07, $25.35, $23.39, $20.60.

6. Find the original data from the stem-and-leaf plot.

7. The winners of the NCAA wrestling championships for the years 1968-1997 are
given in the table below.
a. Compute relative frequencies for each class and fill in the appropriate column
of the table. Round all relative frequencies to 3 decimal places.
b. Draw the relative frequency histogram for the above table.

8. Consider the following relative frequency histogram displaying the number of cars
sold per week last year for a given sales rep, Ronnie, at Emerson Toyota.
Given that there are 52 weeks in a year, approximately how many times did Ronnie
sell 2 cars per week? Round your answer to the nearest whole week.

9. The average retail price for bananas in 1994 was 46.0 cents per pound, as reported
by the U.S. Department of Agriculture. A recent random sample of 8 supermarkets
gave the following prices for bananas in cents per pound.
a. Find the mean price for bananas per pound. Round to 3 decimal places.
b. Find the median price for bananas per pound.
c. Find the mode price for bananas per pound.

10. The number of absences for five children in a local kindergarten class is as follows.
a. Complete the table and use the computing formula
to find the standard deviation for the number of absences. Round to 3 decimal
places. Note: if you would prefer to use the other formula for standard
deviation then adjust the table accordingly.
b. What is the range for the number of absences?
c. Which appears to be a better measure of variation for this data set: range or
standard deviation?
d. What is the variance?

11. True or False.

For the data set {2,3,4,3,6,75}, the median is a better measure of
center than the mean. Explain.

12. Suppose that the mean score on this test is 75.6 with a standard deviation of 7.8.
Suppose also that the scores follow a bell-shaped distribution.
a. Convert a score of 80 to a z-score. Round your answer to 2 decimal places.
b. How many standard deviations is a score of 80 from the mean?

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The solution provides detailed step-by-step calculations and interpretetions of the given statistics problems.

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Statistic Questions

1. The national average of women's times in the 1 mile run is 7.5 minutes with a standard deviation of 1.2 minutes. The male national average is 6.75 minutes with a standard deviation of 0.8 minutes. Your Aunt and Uncle decide to race the mile. His time is 8.35 minutes while
hers is 9.3 minutes. Using the concept of z-scores (z-values), who is the relatively faster runner? Show and explain why.

2. What is the mathematical relationship between standard deviation and variance? Why does it make sense to use the standard deviation (more so than the variance) when discussing real - life data?...for example, dollars, feet, seconds, cars, etc.

3. A multiple choice test (binomial distribution) has 10 questions. Each question has four possible choices. A student guesses the correct answer for each question. Find the probability that the student passes the test if passing is considered to be 6 or more correct.

4. Plywood, Inc. reported these returns on stockholder equity for the past 5 years: 4.3, 4.9, 7.2, 6.7, and 11.6. Consider these as population values.
a. Compute the range, the arithmetic mean, the variance, and the standard deviation.

5. The annual incomes of the five vice presidents of TMV Industries are: $125,000; $128,000;
$122,000; $133,000; and $140,000. Consider this a population.
a. What is the range?
b. What is the arithmetic mean income?
c. What is the population variance? The standard deviation?
d. The annual incomes of officers of another firm similar to TMV Industries were also studied.
The mean was $129,000 and the standard deviation $8,612. Compare the means
and dispersions in the two firms.

CALCULATING THE STATISTICS

6. Construct a histogram, a frequency polygon, and an ogive for the following frequency distribution.
Class Interval Frequency
50-under 60 13
60-under 70 27
70-under 80 43
80-under 90 31
90-under 100 9

7. Construct a stem and leaf plot for the following data.Let the leaf contain one digit.
312 324 289 335 298
314 309 294 326 317
290 311 317 301 316
306 286 308 284 324

8. An examination of rejects shows at least 10 problems. A frequency tally of the problems follows. Construct a Pareto chart for these data.
Problem Frequency
1 673
2 29
3 108
4 379
5 73
6 564
7 12
8 402
9 54
10 202

9. The top music genres according to SoundScan for a recent year are R&B,Alternative (Rock) Music, Rap, and Country. These and other music genres along with the number of albums sold in each (in millions) are shown.
Genre Albums Sold
R&B 146.4
Alternative 102.6
Rap 73.7
Country 64.5
Soundtrack 56.4
Metal 26.6
Classical 14.8
Latin 14.5

Construct a pie chart for these data displaying the percentage of the whole that each of these genres represents.

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