Solve the problem.
Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. If 19 people are randomly selected, find the probability that their mean body temperature will be less than 98.50°F.
(1 point)
Responses
0.3343
0.9826
0.4826
0.0833
To solve this problem, we need to use the Central Limit Theorem to approximate the sampling distribution of the sample mean. First, we calculate the standard error of the mean, which is the standard deviation of the population divided by the square root of the sample size:
Standard error = 0.62 / sqrt(19) = 0.142
Next, we calculate the z-score for a mean of 98.50°F:
z = (98.50 - 98.20) / 0.142 = 2.11
Using a standard normal distribution table or calculator, we find the probability that a z-score less than 2.11 is approximately 0.9826.
Therefore, the probability that the mean body temperature of 19 people will be less than 98.50°F is 0.9826 (Option 1).