Question

Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is σ = 9 days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. What is the expected value for the sampling distribution of the number of school days missed due to influenza?

Answer 1

Answer:

By the Central Limit Theorem, the expected value for the sampling distribution of the number of school days missed due to influenza is 28 days.

Step-by-step explanation:

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

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

The mean of the population is 28 days.

So, by the Central Limit Theorem, the expected value for the sampling distribution of the number of school days missed due to influenza is 28 days.