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In the 19th century, most books quoted "blood heat" as 98 F, until a study published the mean (but not the variance) of a large sample as 36.88 °C. Subsequently, that mean was widely quoted as "37 C". This translates to 98.6 F. (Wikipedia) In a recent study of 148 healthy men and women ages 18-40 years, participating in the Shigella Vaccine Trials at the University of Maryland Center for Vaccine Development, had oral temperatures measured 1-4 times daily for three consecutive days using an electronic digital thermometer. The mean observed oral temperature was 36.8 C which translates to 98.2 F, with a standard deviation of 0.62 F. (Altern Med Rev 2006;11(4):278-293) If you select a person at random from a population with body temperatures that are N(98.2,0.62)... 4. Use the empirical rule to determine the probability that the body temperature is larger than 99.44. Round to 4 decimal places enter your final answer here: ______

Answer :

Final answer:

The probability of selecting a person at random from the population whose body temperature is greater than 99.44°F, as calculated using the empirical rule and the provided mean and standard deviation, is 2.5% or 0.0250.

Explanation:

The empirical rule states that approximately 68% of the data in a normal distribution is within one standard deviation of the mean, 95% is within two standard deviations, and approximately 99.7% is within three standard deviations. Given the mean body temperature from the Shigella Vaccine Trials data is 98.2°F with a standard deviation of 0.62°F, we first need to calculate how many standard deviations away 99.44°F is.

The number of standard deviations away is also referred to as the Z-score. Therefore, we calculate as: Z = (X - μ) / σ = (99.44°F - 98.2°F) / 0.62°F = 2 approximately.

According to the empirical rule, approximately 95% of the data lies within two standard deviations. Since we want to find the probability of the body temperature being larger than 99.44°F (two standard deviations from the mean), we consider the data on the right end of the distribution curve beyond two standard deviations. This consists of the remaining 5% of the distribution. However, since the normal curve is symmetrical, we divide the 5% by two, which gives us 2.5%. Therefore, the probability of a randomly selected person having a body temperature greater than 99.44°F is 0.0250 or 2.5%.

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