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Chapter 6: Q. 2 (page 286)
The percentage of all possible observations of a variable that lie between 25 and 50 equals the area under its density curve between___ and ___expressed as a percentage.
The area under its density curve between 25 and 50 , expressed as a percentage.
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Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarian lifestyle. In the paper "LDL of Taiwanese Vegetarians Are Less Oxidizable than Those of Omnivores" (Journal of Nutrition, Vol. 130, Pp. 1591-1596), S. Lu et al. compared the daily intake of nutrients by vegetarians and omnivores living in Taiwan. Among the nutrients considered was protein. Too little protein stunts growth and interferes with all bodily functions; too much protein puts a strain on the kidneys, can cause diarrhea and dehydration, and can leach calcium from bones and teeth. The daily protein intakes, in grams, for 51 female vegetarians and 53 female omnivores are provided on the Weiss Stats site. Use the technology of your choice to do the following for each of the two sets of sample data.
a. Obtain a histogram of the data and use it to assess the (approximate) normality of the variable under consideration.
b. Obtain a normal probability plot of the data and use it to assess the (approximate) normality of the variable under consideration.
c. Compare your results in parts (a) and (b).
We have provided a normal probability plot of data from a sample of a population. In each case, assess the normality of the variable under consideration.
13. What key fact permits you to determine percentages for a normally distributed variable by first converting to scores and then determining the corresponding area under the standard normal curve?
Students in an introductory statistics course at the U.S. Air Force Academy participated in Nabisco's "Chips Ahoy! 1,000 Chips Challenge" by confirming that there were at least 1000 chips in every 18-ounce bag of cookies that they examined. As part of their assignment, they concluded that the number of chips per bag is approximately normally distributed. Their conclusion was based on the data provided on the Weiss Stats site, which gives the number of chips per bag for 42 bags. Do you agree with the conclusion of the students? Explain your answer. [SOURCE: B. Warner and J. Rutledge, "Checking the Chips Ahoy! Guarantee, " Chance, Vol. 12(1), pp. 10-14]
In the paper "Cloudiness: Note on a Novel Case of Frequency" (Procedings of the Royul Sociery of London, Vol. . pp.), K. Pearson examined data on daily degree of cloudiness, on a scale of 0 to 10 , at Breslau (Wroclaw), Poland, during the decade . A frequency distribution of the data is presented in the following table.
a. Draw a frequency histogram of these degree-of-cloudiness data.
b. Based on your histogram, do you think that degree of cloudiness in Breslau during the decade in question is approximately normally distributed? Explain your answer.
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