Question

The distribution of the amount of change in UF student's pockets has an average of 2.02 dollars and a standard deviation of 3.00 dollars. Suppose that a random sample of 45 UF students was taken and each was asked to count the change in their pocket. The sampling distribution of the sample mean amount of change in students pockets is

A. approximately normal with a mean of 2.02 dollars and a standard error of 3.00 dollars
B. approximately normal with a mean of 2.02 dollars and a standard error of 0.45 dollars
C. approximately normal with an unknown mean and standard error.
D. not approximately normal

Answer 1

B. approximately normal with a mean of 2.02 dollars and a standard error of 0.45 dollars

Explanation:

We use the Central Limit Theorem to solve this question.

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 error
`s = (\sigma)/(√(n))`

In this problem, we have that:

`\mu = 2.02, \sigma = 3, n = 45, s = (3)/(√(45)) = 0.45`

So the correct answer is:

B. approximately normal with a mean of 2.02 dollars and a standard error of 0.45 dollars