Question

Paul plays a video game that is scored by round . In about 500 rounds his career average is 20 points per round with a standard deviation of 5 points per round . Suppose we take random samples of past 3 rounds and calculate the mean number of points scored in each sample . What is the mean and sd of sampling distribibution

Answer 1

Answer:

The mean of the sampling distribution is 20 and the standard deviation is 2.89.

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.

Population:

Mean 20, standard deviation of 5.

Sampling distribution:

3 rounds

Mean = 20

$s = \frac{5}{\sqrt{3}} = 2.89$

The mean of the sampling distribution is 20 and the standard deviation is 2.89.