Stats Problem - Central Limit Theorem

**chrissybee** · February 18th 2009, 06:37 PM

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!!

**mr fantastic** · February 18th 2009, 08:27 PM

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

Thread: Stats Problem - Central Limit Theorem

LinkBack

Thread Tools

Display

Stats Problem - Central Limit Theorem

Similar Math Help Forum Discussions

Central Limit Theorem

central limit theorem problem 2, is this right?

Central Limit Theorem

Central limit Theorem problem (exponential(2))

Central Limit Theorem

Search Tags