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
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Answer #1

Solution: We are given:

μ 24.6, σ 4.8

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

Answer:

large z=rac{x-mu}{sigma}

21 - 24.6 4.8

  0.75

Therefore, the z-score is -0.75

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

Answer:

2 νη

21- 24.6 4.8 25

ー3.6 0,96

  3.75

Therefore, the z-score is -3.75

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

Answer: x and large ar{x} belong to the same distribution

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