# Stats Problem - Central Limit Theorem

• Feb 18th 2009, 06:37 PM
chrissybee
Stats Problem - Central Limit Theorem
An economist wants to estimate the average hourly wage of waitresses in a large metropolitan area. This will be done randomly surveying 250 waitresses and calculating the sample mean. Find the probability that the estimate will be in error by more than 5 cents. Assume that the population's standard deviation is 45 cents.

The answer is .0784 but I don't understand how to get it.

Can someone take me step by step on how to solve this problem?
Thank you so much!!(Happy)
• Feb 18th 2009, 08:27 PM
mr fantastic
Quote:

Originally Posted by chrissybee
An economist wants to estimate the average hourly wage of waitresses in a large metropolitan area. This will be done randomly surveying 250 waitresses and calculating the sample mean. Find the probability that the estimate will be in error by more than 5 cents. Assume that the population's standard deviation is 45 cents.

The answer is .0784 but I don't understand how to get it.

Can someone take me step by step on how to solve this problem?
Thank you so much!!(Happy)

The probability will be equal to $\alpha$ where $\Pr\left( \overline{x} - z_{\alpha/2} \frac{45}{\sqrt{250}} < \mu < \overline{x} + z_{\alpha/2} \frac{45}{\sqrt{250}}\right) = 1 - \alpha$ and $z_{\alpha/2} \frac{45}{\sqrt{250}} = 5$.