Answer: To solve this problem, we need to use the central limit theorem to find the distribution of the sample means. The central limit theorem states that if we take random samples of size n from a population with a mean μ and a standard deviation σ, the distribution of the sample means approaches a normal distribution with a mean of μ and a standard deviation of σ/√n, as n gets larger.
In this case, we have a population of healthy humans with a mean temperature of μ = 98.6 degrees and a standard deviation of σ = 0.8 degrees. We want to find the probability that the average temperature for a sample of 130 healthy people is 98.25 degrees or higher. The sample size is large enough to use the normal distribution to approximate the distribution of the sample means.
The z-score corresponding to a sample mean of 98.25 degrees is:
z = (98.25 - 98.6) / (0.8 / sqrt(130)) = -1.91
Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is greater than -1.91:
P(Z > -1.91) = 0.9719
Therefore, the probability that the average temperature for a sample of 130 healthy people is 98.25 degrees or higher is approximately 0.9719 or 97.19%.
Explanation: