The distribution of actual weights of 8 oz. wedges of cheddar cheese produced at a dairy is Normal with mean 8.1 ounces and standard deviation 0.2 ounces. A sample of 10 of these cheese wedges is selected. What is the probability that the average weight of this sample is between 7.9 and 8.1 ounces?
+118659 The distribution of actual weights of 8 oz. wedges of cheddar cheese produced at a dairy is Normal with mean 8.1 ounces and standard deviation 0.2 ounces. A sample of 10 of these cheese wedges is selected. What is the probability that the average weight of this sample is between 7.9 and 8.1 ounces?
the standard error of the mean is
\(\bar x=8.1\\ SE_{\bar x}=\frac{\sigma}{\sqrt{n}}\\ SE_{\bar x}=\frac{0.2}{\sqrt{10}}\\ SE_{\bar x}=0.0632\\ \)
7.9 is \(- \sqrt{10} = -3.162\) standard errors from the mean
and 8.1 is the mean
This is an area of more thant 3 standard errors below the mean to the mean so the probability is greater than 99.7/2 = 49.85% and less than 0.5%
You could use tables if you want more accuracy.
If you have questions ask and I will try to answer you so that you understand.
