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MAT107Name: StatisticsFinal Exam Prof: FELKER 1. Conceptual Questions a) Give three examples of a continuous random variable. b) Give two examples of a voluntary response sample. Why is a voluntary response sample considered to be a poor sampling technique? 2. Football Player Weights – Listed below are the weights in pounds of 11 players randomly selected from the roster of the Seattle Seahawks when they won Super Bowl XLVIII. Are the results likely to be representative of all National Football League players? Why or why not? 189, 254, 235, 225, 190, 305, 195, 202, 190, 252, 305 For the above data find (a) the mean, (b) the median, (c) the mode, and (d) the midrange. 3. For the grouped frequency distribution below find the (a) mean and (b) modal class. Ages (in years) of Best Actor when an Oscar was won. – 87 male actors, who won an Oscar, were selected and this grouped frequency table was obtained reflecting the age at which the Oscar was won for the particular sample. (Note – Extra columns in the table for your use.) Age (years) when Oscar was won Frequency 20 -29 1 30-39 28 40-49 36 50-59 15 60-69 6 70-79 1 4. Find the range, variance, and standard deviation. Assume the data represent samples, and use the shortcut formula for the unbiased estimator to compute the variance and standard deviation. Hurricanes - Listed below are the numbers of Atlantic hurricanes that occurred in each year. The data are listed in order by year, starting with the year 2000. What important feature of the data is not revealed by any of the measures of variation? 8, 9, 8, 7, 9, 15, 5, 6, 8, 4, 12, 7, 8, 2 5. In the following group frequency distribution, find the variance and standard deviation. Remember to use your shortcut formulas on your green formula sheet you received with your textbook. Ages (in years) of Best Actor when an Oscar was won. – 87 male actors, who won an Oscar, were selected and this grouped frequency table was obtained reflecting the age at which the Oscar was won for the particular sample. (Note – Extra columns in the table for your use.) Age (years) when Oscar was won Frequency 20 -29 1 30-39 28 40-49 36 50-59 15 60-69 6 70-79 1 6. Exam Scores – A final examination for a Statistics course has a mean of 80 and a standard deviation 3. Find the corresponding z score for each raw score. a) 86 b) 77 c) 90 d) 80 7. Rolling Two Dice – If two dice are rolled, one time, find the probability of getting the following results: a) A sum of 5. b) A sum of 8 or 6. c) A sum greater than or equal to 9. 8. Company Volleyball Team - In the ZEST company, which makes designer sneakers, there are 42 employees: 20 are men and 22 are women. If 5 employees are randomly chosen to represent the company in a volleyball team, what is the probability that all the chosen volleyball team members will be women? Would you consider this event to be likely? 9. Find the mean, variance, and standard deviation for this discrete probability distribution. Fun Ways to Flirt – A sociologist randomly selects single adults for different groups of three, and the random variable is the number in the group who say that the most fun way to flirt is in person (based on a Microsoft Instant Messaging survey). 0 0.091 1 0.334 2 0.408 3 0.166 10. If the famous insurance company, Lloyd’s of London, insures a $3 million Monet painting for $5000 per year. And, in each year, the painting has a .00021 chance of being stolen according to the Lloyd’s research team? From Lloyd’s perspective, find the expectation for insuring this painting for one year. 11. Survey on Concern for Criminals – In a survey, 3 of 4 students said the courts show “too much concern” for criminals. Find the probability that at most 1 out of 7 randomly selected students will agree with this statement. 12. Statistics Student Study Time - The average weekly study time for Statistics students is 15 hours. If individual study times are normally distributed with a standard deviation of 5 hours, find the following probabilities. a) A randomly selected Statistics student will study more than 20 hours per week. b) A randomly selected Statistics student will study less than 5 hours per week. 13. Family Entertainment Costs – The mean total costs for all forms of family entertainment (i.e. movies, toys, video games, plays, concerts, etc.) was $12,000 per year. Suppose that and 36 families are randomly selected. Find the probability that the sample mean cost for these 36 families is a) Less than $11,000. b) More than $14,000. c) Between $11,000 and $14,000. 14. Flight Arrivals – Listed below are arrival delays (in minutes) of randomly selected American Airlines flights from New York (JFK) to Los Angeles (LAX). Negative numbers correspond to flights that arrived before the scheduled arrival time. Use a 95% confidence interval. How good is the on-time performance? -5, -32, -13, -9, -19, 49, -30, -23, 14, -21, -32, 11 15. Weights of Bears – The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 54 bears has a mean weight of 195 lb. Assuming that is known to be 130 lb., use a 0.05 significance level to test the claim that the population mean of all such bear weights is greater than 160 lb.