Question

In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a standard deviation of $3,156. Assume the underlying distribution is approximately normal.a. Which distribution should you use for this problem

Answer 1

Answer:

By the Central Limit Theorem, an approximately normal distribution, with mean $6425 and standard deviation $344.35.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

Sample mean was $6,425 with a standard deviation of $3,156

This means that $\mu = 6425, \sigma = 3156$

Sample of 84:

This means that $n = 84, s = \frac{3156}{\sqrt{84}} = 344.35$

a. Which distribution should you use for this problem?

By the Central Limit Theorem, an approximately normal distribution, with mean $6425 and standard deviation $344.35.