Question

10. -10 points JKEStat11 7.E.048 Consider a normal population with the following. (Give your answers correct to two decimal places.) μ-24.6 and σ 4.8 (a) Calculate the z-score for an x of 21. (b) Calculate the z-score for an x of 21 from a sample of size 25. (c) Explain how 21 can have such different z-scores. O x and x belong to the same distribution O x and x belong to different distributions You may need to use the appropriate table in Appendix B to answer this question Need Help? RTaik to Tuter

Answer 1

Solution: We are given:

$\mu=24.6, \sigma=4.8$

(a) Calculate the z-score for an x of 21.

Answer:

$\large z=\frac{x-\mu}{\sigma}$

$\large =\frac{21-24.6}{4.8}$

  $\large =-0.75$

Therefore, the z-score is -0.75

(b) Calculate the z-score for an $\large \bar{x}$ of 21 from a sample of size 25.

Answer:

$\large z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$\large =\frac{21-24.6}{\frac{4.8}{\sqrt{25}}}$

$\large =\frac{-3.6}{0.96}$

  $\large =-3.75$

Therefore, the z-score is -3.75

(c) Explain how 21 can have such different z-scores.

Answer: x and $\large \bar{x}$ belong to the same distribution