Suppose you have the average price for a sample of Lucky Charms at 35 different stores in the valley. Suppose that the population standard deviation for the prices is 1.6. If the population mean is 4.9, what is the z value for a sample average of 4.7?
I don't want you guys to do this for me since it's a homework question, but what formula should I use for this/ which numbers should I plug into the formula I am a bit confused.
Thanks for the help
Standard(ized)/normal/z-scores are given by the following fundamental formula:
$$ z = \frac{x - \mu}{\sigma} $$
where $x$ is a raw score to be transformed, $\mu$ is the mean, and $\sigma$ the standard deviation. The value $x$ comes from the initial distribution based on the question (i.e., "What is the probability that at least $x$ ...").
Now, this question is special in that we are looking at sample means. The only change to make is the following:
$$ z = \frac{\bar{x} - \mu}{\sigma_{\bar{x}}} $$
where $\sigma_\bar{x}$ is the standard error, $\sigma / \sqrt{n}$, with $n$ the sample size. Notice the similarity in both.
You now have enough information to answer the question.