The National Health Statistics Reports dated Oct. 22, 2008, stated that for sample size of 277 18-year-old American males, the sample mean waist circumference was 86.3 cm. A somewhat complicated techniques was employed to determine various population percentiles, resulting in the following values:
5th - 69.6, 10th - 70.9, 25th - 75.2, 50th - 81.3, 75th - 95.4, 90th - 107.1, 95th -116.4
a. Is it plausible that the waist size distribution is at least approximately normal? Discuss your reasoning. If your answer is no, conjecture the shape of population distribution.
b. Assume that the population mean waist size is 85 cm and that population standard deviation is 15cm. How likely is it that a random sample of 277 individuals will result in sample mean waist size of at least 86.3 cm?
c. Referring back to (b), assume now that population mean waist size in 82 cm. Now what is the (approximate) probability that the sample mean will be at least 86.3 cm? In light of this computation, do you think that 82 cm is a reasonable value for µ?