Consider a population with and .

(A) Calculate the z-score for from a sample of size 13.
(B) Could this z-score be used in calculating probabilities using Table 3 in Appendix B of the text? Why or why not?

Values of population not indicated. We do not know what is contained in Table 3. If Table 3 is the one I describe below, the answer is yes, if the distribution is approximately normal.

Z = (score-mean)/SD or SEm for distribution of means.

SEm = SD/√n

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.

To calculate the z-score, we need to know the mean (µ) and standard deviation (σ) of the population.

Since you didn't provide the actual values of the population mean and standard deviation, we'll assume that they are known.

Let's assume:
Population mean (µ) = 100
Population standard deviation (σ) = 15

(A) Calculating the z-score:
To calculate the z-score, we'll use the formula:
z = (x - µ) / σ

Given the sample mean (x) and sample size (n), we can calculate the standard error (SE) as:
SE = σ / √n
Where √n represents the square root of the sample size.

Let's say the sample mean is 110 and the sample size is 13. Using the values from above, we can calculate the z-score as follows:
SE = 15 / √13 ≈ 4.144

z = (110 - 100) / 4.144 ≈ 2.413

So, the z-score for the sample mean of 110 with a sample size of 13 is approximately 2.413.

(B) Could this z-score be used in calculating probabilities using Table 3 in Appendix B of the text?

No, this specific z-score cannot be directly used with Table 3 in Appendix B of the text without further calculations. Table 3 provides the cumulative probabilities up to a z-score of 3.4. However, any z-score beyond that range (like 2.413) would not be directly listed in Table 3.

To calculate probabilities associated with a z-score of 2.413, you would need to use statistical software or a calculator with a built-in normal distribution function. Alternatively, you can use a z-table that provides more detailed values to find the probability associated with the z-score of 2.413.