please explain why these are the correct answers 6.2.13 Question Help The Empiri
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please explain why these are the correct answers
6.2.13 Question Help The Empirical Rule applies rough approximations to probabities for any unimodal symmetric distribution. But for the Normal distribution we can be more precise, as the fgure shows. Use the figure and the fact that the Normal curve is symmetricto answer the questions Do not use a Nomal table or technologk Complete parts a hrough e 2-8 2 a. Roughly what percentage of 2-scores are between 2 and 2? 95% bRoughly what percentage of 2-scores are between -3 and 3? Almost All G. Roughly what percentage of 2-scores are between 1 and 1? 683 d. Roughly what percentage of z-scores are more than O? 50% e.Roughly what percentage of z-scores are between 1 and 2? 135%Explanation / Answer
The 68-95-99.7 rule or the empirical rule says that
68% of data falls within one deviation from the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.
a. As -2 and 2 are 2 standard deviations from the mean, by empirical rule, the percentage of z scores is 95%.
b. As -3 and 3 are 3 standard deviations from the mean, by empirical rule, the percentage of z scores is 99.7% which is almost 100%.
Therefore the answer is almost all.
c. Similarly -1 and 1 are 1 standard deviation from the mean, by empirical rule, the percentage of z scores is 68%.
d. The graph is symmetric and the mean is 0. Therefore, 50% of the scores are more than 0 (and other 50% are less than 0).
e. We saw that 95% scores are between -2 and 2 while 68% are between -1 and 1.
Therefore, the percentage of scores that are from -2 to -1 and 1 to 2
= 95% - 68% = 27%.
=> Percentage of scores that are from 1 to 2 only (the graph is symmetric)
= 27% / 2 = 13.5%.
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