This is my first stats class and I don't know how to do this, could you please help me? Thank you.

You are asked to determine the typical number of sales of a certain product at the store you work for. A sample of 50 days over the last quarter shows an average of 55 units sold per day with a standard deviation of 10 units.
a. Construct a 95 percent confidence interval around the mean.
b. Construct a 99 percent confidence interval around the mean.
c. Show the two limits on a graph of some sort
d. Interpret your results

Of course, I'd be happy to help you with your stats question! Let's go through each part step by step.

a. To construct a 95 percent confidence interval around the mean, we can use the formula:

CI = X̄ ± (z * (σ / √n))

Where:
- CI represents the confidence interval
- X̄ is the sample mean (55 units sold per day)
- z is the z-value corresponding to the desired confidence level (for a 95% confidence level, z = 1.96)
- σ is the population standard deviation (10 units)
- n is the sample size (50 days)

Plugging in the values, we get:
CI = 55 ± (1.96 * (10 / √50))

Now you can calculate the upper and lower limits of the confidence interval.

b. Similarly, to construct a 99 percent confidence interval, we use the same formula but with a different z-value corresponding to the desired confidence level (for a 99% confidence level, z = 2.58):
CI = 55 ± (2.58 * (10 / √50))

Again, calculate the upper and lower limits using this formula.

c. To show the two limits on a graph, you can create a vertical line representing the sample mean (55 units/day) and then add error bars or horizontal lines to represent the upper and lower limits of the confidence intervals for both the 95% and 99% confidence levels.

d. Interpreting the results, the confidence interval represents the range within which we can be X% confident that the true population mean lies. For example:
- In the 95% confidence interval, we can be 95% confident that the true population mean falls somewhere between the lower and upper limits calculated.
- In the 99% confidence interval, we can be 99% confident that the true population mean falls somewhere between the lower and upper limits calculated.

In other words, if we were to repeat the sampling process multiple times, 95% (or 99%) of the confidence intervals calculated would contain the true population mean.

I hope this helps you understand how to calculate and interpret confidence intervals in this scenario. Let me know if you have any further questions!