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Thread: Stats Problem - Central Limit Theorem

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    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!!
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    Quote Originally Posted by chrissybee View Post
    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 $\displaystyle \alpha$ where $\displaystyle \Pr\left( \overline{x} - z_{\alpha/2} \frac{45}{\sqrt{250}} < \mu < \overline{x} + z_{\alpha/2} \frac{45}{\sqrt{250}}\right) = 1 - \alpha$ and $\displaystyle z_{\alpha/2} \frac{45}{\sqrt{250}} = 5$.
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