# Thread: Stats Problem - Central Limit Theorem

1. ## 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!!

2. 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!!
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 $z_{\alpha/2} \frac{45}{\sqrt{250}} = 5$.