Question

A baseball team calls itself "America's Favorite Team," because it has 90,000 fans on social media out of 2,210,000 social media users. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n

Answer 1

Answer:

Population proportion: 0.04

Sampling distribution mean: 0.04n

Sampling distibution standard deviation: 0.196√n

Step-by-step explanation:

The population proportion can be calculated dividing the total number of fans for this team by the total population of fnas in social media:

$\pi=\dfrac{X}{N}=\dfrac{90,000}{2,210,000}\approx0.04$

If we take samples of size n, the mean (or expected value) can be calculated as:

$\mu_s=\pi\cdot n=0.04n$

The standard deviation for the sampling distribution becomes:

$\sigma_s=\sqrt{n\pi(1-\pi)}=\sqrt{n(0.04\cdot 0.96)}=0.196\sqrt{n}$