2. Consider the standard normal curve. (a) What proportion of scores fall betwee

Question

2. Consider the standard normal curve. (a) What proportion of scores fall between z-scores of –1 and +1? (b) What proportion of scores fall below a z-score of 1.2? (c) What proportion of scores fall above a z-score of –0.05? (d) What proportion of scores fall between the mean and a z-score of -2.13?

3. James looks up his score for the last test on the class website and sees that his instructor has posted the scores as percentiles. On the website, James’ score is an 80. Should James be happy or unhappy about how he scored on the test? What does his score mean?

Explanation / Answer

2 a) Proportion of score between -1 and +1 z scores = 0.6827

b) Proportion of score below z score of 1.2 = P(z 1.2) = 0.8849

c) Proportion of scores above z score of -0.05 = 1 - P(z < - 0.05)

= 1 - 0.4801

= 0.5199

d) Proportion of scores between mean and z score of -2.13

= P(z = 0) - P(z = -2.13)

= 0.5 - 0.0166

= 0.4834

3) Perecentile of 80 means, 80% of the people in class have score less marks than James. Since james is in the top 20% of the class, I believe that there is a reasonable cause for him to be happy about the score he have got.

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