Question

For this question, you need to be able to use the zscore table in Appendix B in the Salkind textbook, and apply

the zscore formula (Score – Mean / SD = zscore) in figuring out the percentile position of scores.  You may also want to review the slides on hypothesis testing, and the handout problems, which show you the steps.

Hint: You must always remember important rules in translating zscores to percentile position:

(a) Mean score = z = 0, but that position occurs at 50th percentile; always!,

(b) If z-score is positive , then that positive zscore occurs at a percentile above the mean score (at a percentile that is higher than the mean score!).

(c) If z-score is negative, then that negative zscore occurs at a percentile below the mean score

(d) For example, you should be able to figure out that a score 1 SD above the mean corresponds 1z, and that corresponds to 34.13% area in the table between the mean and the zscore of 1, and therefore, the score will be found at 84.13th percentile.

Now, let’s consider that a researcher studies the “length of homelessness” of adult individuals. Shelter X will take individuals who are homeless, and based on their statistics that they collect for the length of  homelessness prior to entering into the shelter, the homelessness Mean = 50 days, SD = 10.5 days for individuals, who do well in the shelter.

The shelter director notes that those individuals who come to the shelter with “their prior length of homelessness” that is greater (>) than 3 SD from the shelter “average” length of prior homelessness, typically do not do well, and need many other kinds of support services that the shelter is not currently able to provide.

Answer questions below:

(a) At what percentile of prior length of homelessness is “Tarik” who reports that he has been homeless for 85 days? Explain and show how you derived/calculated your answer:

[Hint: 85 – 50 / 10.5 = _zscore]

Answer:

(b) At what percentile of prior length of homelessness is “Omar” who reports that he has been homeless for 63 days? Explain and show how you derived/calculated your answer:

Answer:

(c) Now, consider both Tarik’s and Omar’s prior homelessness, and explain, which of these two men is more likely to benefit by shelter services and which one is not, and why?

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