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

Answer 2

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

Given

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.

Central limit theorem;

Central limit theorem is a statistical theory which states that when the large sample size is having a finite variance, the samples will be normally distributed and the mean of samples will be approximately equal to the mean of the whole population.

The standard error is calculate by following formula;

$\rm Standard \ error=\dfrac{\sigma}{\sqrt{n} }$

Where the value of $\sigma$ = 100 and n = 40.

Substitute all the values in the formula;

$\rm Standard \ error=\dfrac{\sigma}{\sqrt{n} }\\\\\rm Standard \ error=\dfrac{1000}{\sqrt{40} }\\\\\rm Standard \ error=158..11$

Hence, approximately Normal, with a mean of 950 and a standard error of 158.11.

To know more about standard error click the link given below.

https://brainly.com/question/2634651