Question

The mean GPA for 112 residents of the local apartment complex is 1.7. What is the best point estimate for the mean GPA for all residents of the local apartment complex

Answer 1

By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.

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 = (\sigma)/(√(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 sample of 112 residents has a mean GPA of 1.7.

By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.