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(Solved): Assume that human body temperatures are normally distributed with a mean of 98.19F and a standar ...



Assume that human body temperatures are normally distributed with a mean of \( 98.19^{\circ} \mathrm{F} \) and a standard dev
Assume that human body temperatures are normally distributed with a mean of and a standard deviation of . a. A hospital uses as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage suggest that a cutoff of is appropriate? b. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only of healthy people to exceed it? (Such a result is a false positive, meaning that the test result is positive, but the subject is not really sick.) . D. Yes, because there is a large probability that a normal and healthy person would be considered to have a fever. b. The minimum temperature for requiring further medical tests should be people to exceed it. (Round to two decimal places as needed.)


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To solve these problems, we will use the properties of the normal distribution. a. To find the percentage of normal and healthy persons considered to have a fever, we need to calculate the percentage of individuals whose body temperature is greater than or equal to 100.6°F. First, we need to standardize the temperature value using the formula: z = (x - ?) / ? where: z is the standardized score, x is the temperature value, ? is the mean of the distribution, and ? is the standard deviation of the distribution. Using the given values: x = 100.6°F ? = 98.19°F ? = 0.64°F Calculating the standardized score: z = (100.6 - 98.19) / 0.64 z ? 3.77
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