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Answer :
Final answer:
The proportion of healthy adults expected to have body temperatures below 97.8°F is 2.5%, since it is two standard deviations below the mean. However, in the context of the options given, which seem to imply the proportion below the mean, the correct answer would be 50%. the correct answer from the options is D) 0.95,
Explanation:
To ascertain the proportion of healthy adults expected to have body temperatures below 97.8 degrees Fahrenheit, we utilize the concept of standard distribution, as body temperature is known to distribute normally in healthy adults. The information provided suggests that the mean body temperature is 98.4°F with a standard deviation of 0.3°F. Based on this, 97.8°F is two standard deviations below the mean (98.4 - 2(0.3) = 97.8°F).
According to the empirical rule (68-95-99.7 rule) for normal distributions, approximately 95% of the values lie within two standard deviations of the mean. This implies that 2.5% are below this range. Hence, the correct answer from the options is D) 0.95, since we expect around 95% to have body temperatures above 97.8°F, leaving 5% (100% - 95%) below this temperature. As we only account for the lower portion here, we take half of 5%, which results in 2.5% or 0.025 of healthy adults expected to have a body temperature below 97.8°F. However, the options given might be misleading unless we're considering the proportion below the mean, which from the options, would be 50% as represented by option A) 0.50.
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