#3. Birth Weights Birth weights in the United States have a distribution that is approximately normal with a mean of 3369 g and
a standard deviation of 567 g (based on data from “Comparison of Birth Weight Distributions between Chinese and Caucasian Infants,” by Wen, Kramer, Usher, American Journal of Epidemiology, Vol. 172, No. 10). a. One definition of a premature baby is that the birth weight is below 2500 g. If a baby is randomly selected, find the probability of a birth weight below 2500 g.
b. Another definition of a premature baby is that the birth weight is in the bottom 10%. Find the birth weight that is the cutoff between the bottom 10% and the top 90%.
c. A definition of a “very low birth weight” is one that is less than 1500 g. If a baby is randomly selected, find the probability of a “very low birth weight.”
d. If 25 babies are randomly selected, find the probability that their mean birth weight is
greater than 3400 g.
#28. Medication Usage In a survey of 3005 adults aged 57 through 85 years, it was found that 81.7% of them used at least one prescription medication (based on data from “Use of Prescription and Over-the-Counter Medications and Dietary Supplements Among Older Adults in the United States,” by Qato et al., Journal of the American Medical Association, Vol.300, No. 24).
a. How many of the 3005 subjects used at least one prescription medication?
b. Construct a 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication.
c. What do the results tell us about the proportion of college students who use at least one prescription medication?
#15 . Garlic for Reducing Cholesterol In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg/dL) had a mean of 0.4 and a standard deviation of 21.0 (based on data from “Effect of Raw Garlic vs Commercial Garlic Supplements on Plasma Lipid Concentrations in Adults with Moderate Hypercholesterolemia,” by Gardner et al., Archives of Internal Medicine, Vol. 167). Construct a 98% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
Follow these procedures for the two numbers: a. Use given values of the population mean and standard deviation to solve for the z-score. The z-score table can then be used to solve for the probability.
b. For probability corresponding to 10% and 90%, the z-scores are obtained. The z-score is then obtained to get the limits of the weight.
c. The Markov's inequality can be used since the variable is random. Simply divide 1500 by 3369.
