It looks like you uploaded an image related to a statistics problem asking you to perform a Z-test and find the p-value. Here's a breakdown of the problem and steps involved:

1. Z-Test Formula: $Z = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$ Where:

   • $\bar{X}$ is the sample mean.
   • $\mu$ is the population mean.
   • $\sigma$ is the population standard deviation.
   • $n$ is the sample size.

2. P-Value: The p-value is the probability that the test statistic (Z) falls within the observed distribution under the null hypothesis. The area under the curve to the left of the calculated Z-score gives the p-value.

3. Steps on the Image:

   • Step 1: Choose between a one-tailed or two-tailed test. A two-tailed test is chosen in your case.
   • Step 2: Input the Z-score (rounded to 3 decimal places).
   • Step 3: The shaded region under the curve represents the p-value.
   • Step 4: Input the calculated p-value (rounded to 3 decimal places).

Let me know the Z-score or any other values you have, and I can help you calculate the p-value. Alternatively, I can guide you through the process of solving it.

Would you like details on how to calculate this or have any questions?

Here are 5 related questions for further exploration:

1. What is the difference between one-tailed and two-tailed tests?
2. How is the Z-score related to confidence intervals?
3. Why is the normal distribution used in Z-tests?
4. What is the significance level ($\alpha$) and how does it relate to the p-value?
5. How do we interpret the p-value in hypothesis testing?

Tip: Always check whether your test should be one-tailed or two-tailed. This impacts the area you calculate under the curve and the corresponding p-value.