Question

Find the reliability factor, Zα/2, to estimate the mean, of a normally distributed population with a known population variance for the following.

A) 81% confidence level
B) 86% confidence level
C) 80% confidence level

Answer 1

To find the reliability factor, you need to determine the z-score corresponding to the desired confidence level. The z-score can be found using a standard normal probability table or a calculator. For 81% confidence level, the reliability factor is approximately 1.41. For 86% confidence level, the reliability factor is approximately 1.56. For 80% confidence level, the reliability factor is approximately 1.28.

Step-by-step explanation:

The reliability factor, Zα/2, is used to estimate the mean of a normally distributed population with a known population variance. To find the reliability factor, we need to determine the z-score corresponding to the desired confidence level. The z-score can be found using a standard normal probability table or a calculator.

1. For the 81% confidence level, the area in the tails is 0.19. Since the distribution is symmetric, each tail will have an area of 0.095. Therefore, the z-score corresponding to this confidence level is approximately 1.41.
2. For the 86% confidence level, the area in the tails is 0.14. Each tail will have an area of 0.07. The z-score corresponding to this confidence level is approximately 1.56.
3. For the 80% confidence level, the area in the tails is 0.20. Each tail will have an area of 0.10. The z-score corresponding to this confidence level is approximately 1.28.