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A Waist is a Terrible Thing to Mind: The waist circumference of males 20 to 29 years ele is approximately normally distributed, with mean 92.5 cm and standard deviation 13.5 Source: M.A. McDowell. CD. Fryar.R. Hirs for Children and Adults: U.S. Population. 1999-2002. Advance data from vital and health statistics: No. 361. Hyattsville, MD: National Center for Health Statistics, 2005. d CL. Ogden, Anthropometric Reference Data 5. Draw a normal curve with the parameters labeled. 92.5 What proportion of 20- to 29-year-old males have a waist circumference that is less than 100 cm? ls this measurement unusual? 6. What is the probability a randomly selected 20-to 29-year-old male has a circumference between 80 and 100 cm? 7. waist Determine the waist circumferences that represent the middle 90% of all waist circumferences? 8.
Exam Cutoffs: Suppose the scores earned on a professors final exam are normally distributed with mean 60 and standard deviation 5. The professor assigns the grades for this exam as follows: The top 6% get an A, the next 14% get a B, the middle 60% get a C, the bottom 6% fail, and the rest earn a D. Determine the cutoffs for this professors exam. In other words, find the following values. 9. What are the scores between which a student would end up earning a C? 10. What is the highest score a student can have and still ailthe class? 11. What is the lowest score a student can have and still obtain an A? 12. What are the scores between which a student would end up earning a B?
eni Smokers. According to the National Center for Health Statistics (2004), 22% ofadultan smokers. A random sample of 400 adults is obtained. 13. Describe the sampling distribution of p, the sample proportion of adults who smoke Be sure to draw the graph for the sampling distribution below. 14. In a random sample of 400 adults, what is the probability that at least 40 are smokers. Is this value unusual? Soda Bottles: A machine used for filling plastic bottles with a soft drink has a known standard deviation of: 0.06 liter. The target mean fill volume is μ 2.0 liters. 15. Describe the sampling distribution of R, the sample mean of liters in a soft drink bottle. Be sure to draw the graph for the sampling distribution below. 16. A quality-control manage r obtains a random sample of 36 bottles. He will shut down the machine if the sample mean of these 36 bottles is less than 1.97 liters or greater than 2.02 liters. What is the probability that the quality-control manager will shut down the machine even though the machine is correctly calibrated?
How Much Do You Read? A Gallup poll conducted July 21-August 14,1978, asked 1225 Americans, During the past year, about how many books, either hardcover or paperbac did you read either all or part of the way through? Results of the survey indicated that - 18 books and s 7 books. 17. Describe the distribution. Be sure to draw the graph of the distribution. 18, Construct and interpret a 99% confidence interval for the mean number of books Americans read either all or part of during the preceding year Marketing: Suppose the marketing company did do a survey. They randomly surveyed 200 households and found that in 120 of them, the woman made the majority of the purchasing decisions. We are interested in the population proportion of households where women make the majority of the purchasing decisions. 19. Describe the distribution. Be sure to draw the graph of the distribution. 20. Construct and interpret a 90% confidence interval for the population proportion of households where the women make the majority of the purchasing decisions
Medicine: A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of nine patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.7;2.8; 3.0; 2.3;2.3;2.2; 2.8; 2.1; and 2.4. 21. Describe the distribution. Be sure to draw the graph of the distribution. 22. Construct and interpret a 95% confidence interval for the population mean length of time. Be sure to sketch the graph of the distribution and state the confidence interval and its interpretation. Too Much Phone Time: Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. 23. Do teenagers spend more time on their phone now? Conduct the appropriate hypothesis test. Be sure to sketch the graph and include and interpret the p-value in your conclusion at a significance level of a0.10
or Appearance? Over the past few decades, public health officials have examined ieli k between weight concerns and teen girls smoking and found that about 30% of teen the dirls smoke to stay thin. Researchers surveyed a group of 300 randomly selected teen girs living in Massachusetts (between 12 and 15 years old), 25% of the sample said they smoked to stay thin. 24. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin? Conduct the appropriate hypothesis test. Be sure to sketch the graph and include the p-value in your conclusion if a0.01. Family Size: According to the N.Y. Times Almanac the mean family size in the US. is 3.18. A sample of a college math class resulted in the following family sizes: 5; 4; 5;4; 4;3; 6, 4; 3;3;5;5;6; 3;3; 2;7:4; 5: 2; 2; 2;3;2 a 0.05 level, is the class mean family size greater than the national average? Conduct the appropriate hypothesis test. Be sure to sketch the graph and include the p-value in your conclusion if a 0.05. Does the Almanac result remain valid? Why or why not? 25. At
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Answer #1

(5)

52 65.5 79 92.5 106 119.5 133

(6)

52 63.3 79 92.5 106 119.5 133 Area from a value (Use to compute p from Z) Value froman area (Use to compute Z for confidence intervals) Specify Parameters Mean 92.5 SD 13.5 Above1.96 O Below 100 Between -1.96 Outside -1.96 and 1.96 and 1.96 Results Area (probability) 0.7107

The proportion is 0.7107. This is not unusual.

(7)

Probability = 0.5335

(8)

52 63.3 92.3 106 119.5 133 Aa from a value (Use to compute p from Z) Value from an area (Use to compute Z for confidence intervals) Specify Parameters Area 0.90 Mean 92.5 SD 13.5 Results Recalculate O Above Below Between 70.29 and 114.71 O Outside

The measurements are 70.29 cm and 114.71 cm.

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