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Solution:

For these data x−=3.46 and s = 1.348. The first observation x = 1.6 in the data set has z-score

z=(x-x−)/s=(1.6−3.46)/1.348=−1.38

which means that x = 1.60 is 1.38 standard deviations below the sample mean. The second observation x = 5.2 has z-score

z=(x-x−)/s=(5.2−3.46)/1.348=1.291

which means that x = 5.2 is 1.291 standard deviations above the sample mean. Repeating the process for the remaining observations gives the full set of z-scores

-1.38 1.291 -0.49 0.18 0.40 Please let me know if you need any clarification. I'm always happy to answer your questions.

Sep 10th, 2015

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