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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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