Question

The body temperatures of adults have a mean of 98.6°F and a standard deviation of 0.60° F. Describe the center and variability of the sampling distribution of the sample mean for a random sample of 50 adults. center = 98.6, variability = 0.14 center = 98.6, variability = 0.07 center = 0.60, variability = 0.07 center = 98.6, variability = 0.008 center = 98.6, variability = 0.08

Answer 1

Answer:

center = 98.6, variability = 0.08

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

The center is the mean.

So $\mu = 98.6$

The standard deviation of the sample of 50 adults is the variability, so

$s = \frac{0.6}{\sqrt{50}} = 0.08$

So the correct answer is:

center = 98.6, variability = 0.08