The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.60° F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater
Than 98.4° F.
A)0.9772
B)0.0228
C)0.8188
D)0.9360

Question

Quizplus · Accepted Answer

Using the Central Limit Theorem, we can calculate the probability that the mean body temperature of 36 randomly selected adults is greater than 98.4°F. The standard error of the mean (SEM) is the standard deviation divided by the square root of the sample size, which is 0.60 / sqrt(36) = 0.10. The Z-score for 98.4°F is (98.4 - 98.6) / 0.10 = -2. The probability of a Z-score being greater than -2 is 0.9772, indicating the likelihood that the mean temperature of the sample is above 98.4°F.

The Body Temperatures of Adults Are Normally Distributed with a Mean