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

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 and standard deviation , a large sample size can be approximated to a normal distribution with mean and standard deviation, which is also called standard error .

In this problem, we have that:

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

By the Central Limit Theorem, approximately normal with mean and standard error

So the correct answer is:

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