Question

b) According to a certain​ survey, adults spend 2.35 hours per day watching television on a weekday. Assume that the standard deviation for​ "time spent watching television on a​ weekday" is 1.93 hours. If a random sample of 60 adults is​ obtained, describe the sampling distribution of x overbar​, the mean amount of time spent watching television on a weekday

Answer 1

Answer:

Normally distributed, with mean 2.35 hours per day and standard deviation 0.2492.

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.

Sampling distribution

By the Central Limit Theorem, normally distributed, with mean 2.35 hours per day and standard deviation $s = \frac{1.93}{\sqrt{60}} = 0.2492$.