Consider a population with µ=93.3 and σ=5.27.
(A) Calculate the z-score for x=94.9 from a sample of size 12.
(B) Could this z-score be used in calculating probabilities using Table 3 in Appendix B of the text? Why or why not?
(A) z = (x - mean)/(sd/√n)
With your data:
z = (94.9 - 93.3)/(5.27/√12)
I'll let you finish the calculation.
(B) Do not have access to the table.
To calculate the z-score for x=94.9 from a sample of size 12, we need to use the formula:
\[ z = \frac{x - \mu}{\frac{\sigma}{\sqrt{n}}} \]
where:
- \( z \) is the z-score
- \( x \) is the value you want to find the z-score for (in this case, 94.9)
- \( \mu \) is the population mean (given as 93.3)
- \( \sigma \) is the population standard deviation (given as 5.27)
- \( n \) is the sample size (given as 12)
(A) Plugging in the values into the formula, we get:
\[ z = \frac{94.9 - 93.3}{\frac{5.27}{\sqrt{12}}} \]
Calculating this, the z-score is approximately 1.60.
(B) This z-score can be used in calculating probabilities using Table 3 in Appendix B of the text, but with some limitations.
Table 3 in Appendix B usually provides the area under the standard normal curve from the left tail (i.e., to the left of the z-score). It does not provide the exact probability for any arbitrary z-score. However, we can still estimate the probability by finding the closest z-score in the table and using the provided values.
Using the table, you can find the closest z-score to 1.60 and the corresponding probability. However, keep in mind that this is only an estimation and may not be completely accurate.
If you need more accurate probabilities, you can use statistical software or calculators that can calculate probabilities based on the z-score more precisely.