Question

The distribution of the amount of money in savings accounts for University of Alabama students has an average of 950 dollars and a standard deviation of 1,000 dollars. Suppose that we take a random sample of 40 University of Alabama students and ask them how much they have in their savings account. The sampling distribution of the sample mean amount of money in a savings account is Group of answer choices approximately Normal, with a mean of 950 and a standard error of 1000 Not approximately normal Approximately Normal with an unknown mean and standard error approximately Normal, with a mean of 950 and a standard error of 158.11

Answer 1

Answer:

Approximately Normal, with a mean of 950 and a standard error of 158.11

Step-by-step explanation:

To solve this question, we need to understand the Central Limit Theorem.

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation, which is also called standard error $s = \frac{\sigma}{\sqrt{n}}$.

In this problem, we have that:

$\mu = 950, \sigma = 1000$

The sampling distribution of the sample mean amount of money in a savings account is

By the Central Limit Theorem, approximately normal with mean $\mu = 950$ and standard error $s = \frac{1000}{\sqrt{40}} = 158.11$

So the correct answer is:

Approximately Normal, with a mean of 950 and a standard error of 158.11