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Difficulty:
95%
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Question Stats:
37% (01:47) correct
63%
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A set of test scores at a large university is normally distributed with a mean of 74 and a standard deviation of 7. Which of the following is true?
I. More students scored above 83 than scored below 63.
II. At least 65% of students scored between 67 and 81.
III. More than half the students scored above 75.
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
I. More students scored above 83 than scored below 63.
II. At least 65% of students scored between 67 and 81.
III. More than half the students scored above 75.
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
30 Sep 2021, 09:11
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Bunuel
One thing to note is test scores are likely integers, so we will not have a perfectly normal distribution.
I. The normal distribution is symmetrical. 83 is 9 higher than 74. 63 is 11 below 74. Then 83 is closer, and more students would be in the closer cutoff, so this is true.
II. We know roughly 68% of the data lies within one standard deviation of the mean. Both 67 and 81 are exactly 1 standard distribution away from 74, so we can say including values 67 and 81, the values between 67 and 81 cover at least 68% of the data. Yet the word "between" does not specify whether we include 67 and 81, so this is not always true if we give 67 and 81 each a 2% weight.
III. We know less than half scored higher than 75. In fact, less than half scored higher than 74 since there will be people who scored exactly 74.
Ans: A
03 Nov 2021, 07:55
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