Davina D.

asked • 04/18/16

Can someone check this

Exam scores from a previous STATS 200 course are normally distributed with a mean of 74 and standard deviation of 2.65. Approximately 95% of its area is within:

a. One standard deviation of the mean

b. Two standard deviations of the mean

c. Three standard deviations of the mean

d. Depends on the number of outliers

e. Must determine the z-scores first to determine the area
 
Wouldn't this answer be two standard deviations of the mean. Sine the one standard would be 68% while the third would be 99.7%.

1 Expert Answer

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Kenneth S. answered • 04/18/16

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Davina D.

how did you come up with 0.9545 did you use the mean±(2x*2.65) equation
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04/18/16

Kenneth S.

You need to review material on the Normal Distribution (and the Standard Normal Distribution), and meaning of standard deviation.  Briefly, every writeup on this subject will tell you that about 68.3% of data falls between -1 s.d. and +1 s.d. when the distribution is normal, and 95.45% of the data falls between -2 s.d. & +2 s.d.
 
I strongly suggest that you Google this subject and read materials that come to light in that search. Wikipedia, among others, as well as your own textbook (it is to be hoped that your class uses such a thing) should make this very clear, including with illustrations (graphs, area under curves, tables, etc.
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04/18/16

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