Many body measurements of people of the same sex and similar ages such as height and upper arm length follow a Normal distribution reasonably closely. Weights, on the other hand, are not Normally distributed. Suppose a survey includes the weights of a representative sample of 548 females in the United States aged 20 – 29 . Suppose the mean of the weights was 161.58 pounds, and the standard deviation was 48.95 pounds. The histogram of the data includes a smooth curve representing an (161.58,48.95) distribution. The graph shows a histogram with an overlying Normal curve. The horizontal axis is labeled “Weight in pounds” and shows values from 50 to 400, in increments of 50. The vertical axis is labeled “Number in sample” and shows values from 0 to 160, in increments of 20. There are 11 bars on the histogram that span from 75 pounds on the horizontal axis to 400 pounds. Each bar covers an interval of 25 pounds. The bar in the interval of 75 to 100 pounds has a number in the sample of around 15. The bar in the interval of 100 to 125 pounds reaches to approximately 85 on the vertical axis. The bar in the interval of 125 to 150 pounds reaches to approximately 125 on the vertical axis. The bar in the interval of 150 to 175 pounds reaches to approximately 95 on the vertical axis. The bar in the interval of 175 to 200 pounds reaches to approximately 50 on the vertical axis. The bar in the interval of 200 to 225 pounds reaches to approximately 30 on the vertical axis. The bar in the interval of 225 to 250 pounds reaches to approximately 20 on the vertical axis. The bar in the interval of 250 to 275 pounds reaches to approximately 10 on the vertical axis. The bar in the interval of 275 to 300 pounds reaches to approximately 5 on the vertical axis. The bar in the interval of 300 to 325 pounds reaches to approximately 8 on the vertical axis. The bar in the interval of 325 to 350 pounds reaches to approximately 2 on the vertical axis. The bar in the interval of 350 to 375 pounds reaches to approximately 1 on the vertical axis. The bar in the interval of 375 to 400 pounds reaches to approximately 1 on the vertical axis. To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt! From the histogram, the Normal curve does not appear to follow the pattern in the histogram that closely. Because of this, the use of areas under the Normal curve may not provide a good approximation to weights in various intervals. You may find Table A useful. (a) There were 13 females that weighed under 100 pounds. What percent of females aged 20 to 29 weighed under 100 pounds? (Enter your answer rounded to two decimal places.) percent under 100 lbs: % What percent of the (161.58,48.95) distribution is below 100 ? (Enter your answer rounded to two decimal places.) percent below 100 : % (b) There were 33 females that weighed over 250 pounds. What percent of females aged 20 to 29 weighed over 250 pounds? (Enter your answer rounded to two decimal places.) percent over 250 lbs: % What percent of the (161.58,48.95) distribution is above 250 ? (Enter your answer rounded to two decimal places.) percent above 250 : % (c) Based on your answers in parts (a) and (b), do you think it is a good idea to summarize the distribution of weights by an (161.58,48.95) distribution? No, because the sample size is too small. No, because the predicted percentages are significantly different than the actual percentages. Yes, because the predicted percentages are not significantly different from the actual percentages. Yes, because most females weigh between 100 pounds and 250 pounds. Question So