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zysi [14]
3 years ago
7

The distribution of the amount of money in savings accounts for Florida State students has an average of 1,200 dollars and a sta

ndard deviation of 900 dollars. Suppose that we take a random sample of 10 Florida State 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
Mathematics
1 answer:
Anestetic [448]3 years ago
7 0

Answer:

By the Central Limit Theorem, the sampling distribution of the sample mean amount of money in a savings account is approximately normal with mean of 1,200 dollars and standard deviation of 284.6 dollars.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes 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 = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Average of 1,200 dollars and a standard deviation of 900 dollars.

This means that \mu = 1200, \sigma = 900

Sample of 10.

This means that n = 10, s = \frac{900}{\sqrt{10}} = 284.6

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

By the Central Limit Theorem, approximately normal with mean of 1,200 dollars and standard deviation of 284.6 dollars.

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