Answer :
Final answer:
The empirical rule was used to calculate probabilities of body temperatures within a normal distribution with a mean of 98.6. These probabilities are estimates and can vary based on the standard deviation used.
Explanation:
The empirical rule, also known as the 68-95-99.7 rule, is used in statistics and it provides a quick estimate of the probability of a certain outcome in a normal distribution, based on how many standard deviations the outcome is from the mean.
a) For the probability that the body temperature is less than 97.58, we would look at the average normal body temperature of 98.6 (which would be our mean) and assuming a standard deviation of 1. If 97.58 is within one standard deviation from the mean, then we can use the empirical rule to estimate that about 34% of body temperatures are below 97.58, because about 68% of values lie within one standard deviation of the mean and we are only looking at the lower half.
b) The probability that the body temperature is between 98.2 and 99.44, again assuming a standard deviation of 1, we can estimate that about 47.5% of body temperatures lie within this range, because 99.44 is within one standard deviation from the mean (34% below and 13.5% above, according to the empirical rule)
c) The probability that the body temperature is between 97.58 and 99.44 would be about 68% according to the empirical rule.
d) The probability that the body temperature is larger than 99.44 would be about 13.5%, because according to the empirical rule, it lies within one standard deviation above the mean.
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