Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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

Sagot :

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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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 [tex]\mu = 6425, \sigma = 3156[/tex]

Sample of 84:

This means that [tex]n = 84, s = \frac{3156}{\sqrt{84}} = 344.35[/tex]

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.