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figure out the percentile based on the z score

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1. A sample of 148 of our statistics students rated their level of admiration for Hilary Rodham Clinton on a scale of 1 to 7. The mean rating was 4.06 and the standard deviation was 1.70. (For this exercise, treat this sample as the entire population of interest).

a. use these data to demonstrate that the mean of the z distribution is always 0.
b. use these data to demonstrate that the standard deviation of the z distribution is always 1.
c. calculate the z score for student who rated his admiration of Hilary Rodham Clinton as 6.1.
d. a student had a z score of -0.55. What rating did she give for her admiration of Hilary Rodham Clinton?

2. Georgiou and colleagues (1997) reported that college students had healthier eating habits, on average, than did those who were neither college students nor college graduates. The 412 students in the study ate breakfast a mean of 4.1 times per week with a standard deviation of 2.4. For this exercise, imagine that this is the entire population of interest; thus these numbers can be treated as parameters.
a. roughly, what is the percentile for a student who eats breakfast four times per week?
b. roughly, what is the percentile for a student who eats breakfast six times per week?
c. roughly, what is the percentile for a student who eats breakfast twice a week?

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Test and Measurements Task

See attached chart. Your assistance is greatly appreciated. Thank you.

TASK
You have been provided the z-scores of three individuals.
1. Person A received a z-score of 1.0.
2. Person B received a z-score of 0
3. Person C received a z-score of -1.0.

Using Figure above (see attchement), indicate each individual's score as a T score, CEEB score, IQ score, and approximate percentile score. Once you have indicated these transformed scores, in 1-2 pages, describe why it is possible to easily convert standard scores from one scale to another. Include in your answer the mean and standard deviation of each of the transformed scores and the theoretical rationale for their equivalency.

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