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Week Four Quiz 1. Which of the following statements are correct? a. A normal distribution is any distribution that is not unusual. False b. The graph of a normal distribution is bell-shaped. True c. If a population has a normal distribution, the mean and the median are not equal. False d. The graph of a normal distribution is symmetric. True Using the 68-95-99.7 rule: Assume that a set of test scores is normally distributed with a mean of 100 and a standard deviation of 20. Use the 68-95-99.7 rule to find the following quantities: Suggest you make a drawing and label first… a. Percentage of scores less than 100 50% b. Relative frequency of scores less than 120 87% c. Percentage of scores less than 140 97.5% d. Percentage of scores less than 80 16% e. Relative frequency of scores less than 60 2.5% f. Percentage of scores greater than 120 16% 2. Assume the body temperatures of healthy adults are normally distributed with a mean of 98.20 °F and a standard deviation of 0.62 °F (based on data from the University of Maryland researchers). a. If you have a body temperature of 99.00 °F, what is your percentile score? 99 degrees would be at the 90th percentile b. Convert 99.00 °F to a standard score (or a z-score). Z (99) = (99-98.2)/0.62 = 1.2903 or 1.29 c. Is a body temperature of 99.00 °F unusual? Why or why not? The temperature of 99.00 degrees is just 1.29 more than the mean therefore it wouldn’t be regarded as very uncommon. d. Fifty adults are randomly selected. What is the likelihood that the mean of their body temperatures is 97.98 °F or lower? P= 0.0061 e. A person’s body temperature is found to be 101.00 °F. Is the result unusual? Why or why not? What should you conclude? The body temperature of 101.00 degrees is 4.52 more than the mean consequently it would be regarded as a little uncommon. Z (101) = (101-98.2)/0.62 = 4.5161 f. What body temperature is the 95th percentile? X = 99.2199 or 99.2 degrees g. What body temperature is the 5th percentile? X = 97.1801 or 97.2 degrees h. Bellevue Hospital in New York City uses 100.6 °F as the lowest temperature considered to indicate a fever. What percentage of normal and healthy adults would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6 °F is appropriate? P = 0.9999 In accordance to the p value less than 0.01% of the grown persons will have a temperature this high hence, a lower cutoff must be thought about.