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10 Oct 2025, 00:24
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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?
Indicate all that apply.
A. More students scored above 83 than scored below 63.
B. At least 65% of students scored between 67 and 81.
C. More than half the students scored above 75.
Indicate all that apply.
A. More students scored above 83 than scored below 63.
B. At least 65% of students scored between 67 and 81.
C. More than half the students scored above 75.
Updated on: 11 Oct 2025, 07:15
Originally posted by Sajjad1994 on 11 Oct 2025, 07:14.
Last edited by Sajjad1994 on 11 Oct 2025, 07:15, edited 1 time in total.
Last edited by Sajjad1994 on 11 Oct 2025, 07:15, edited 1 time in total.
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Official Explanation
A normal curve is symmetrical about the mean. The number 63 is farther from the mean of 74 than is the number 83, because 74 – 63 = 11, but 83 – 74 = only 9. Then 63 represents a more remote or extreme score, and fewer students score below 63 than above 83, making (A) correct.
Alternately, there is less area in the tail to the left of 63 than in the tail to the right of 83. (B) is correct by the “rule of 68 – 95 – 99.7.” In a normal distribution, about 68% of the data falls within 1 standard deviation of the mean. The numbers 81 = 74 + 7 and 67 = 74 – 7 are exactly the values 1 standard deviation above and below the mean. So about 68% of students will score within that interval, 68% >65%.
Finally, (C) is not correct. In a normal distribution, 50% of the data is above the mean and 50% is below the mean. If about 50% of students score above 74, then fewer than 50% of students will score above the higher number, 75. A correct statement might have read, “More than half the students scored above 70.” (Since 70 < 74 = the mean.)
Answer is (A) and (B).
GMAT-Club-Forum-6a62qqvu.png [ 212.41 KiB | Viewed 40 times ]
A normal curve is symmetrical about the mean. The number 63 is farther from the mean of 74 than is the number 83, because 74 – 63 = 11, but 83 – 74 = only 9. Then 63 represents a more remote or extreme score, and fewer students score below 63 than above 83, making (A) correct.
Alternately, there is less area in the tail to the left of 63 than in the tail to the right of 83. (B) is correct by the “rule of 68 – 95 – 99.7.” In a normal distribution, about 68% of the data falls within 1 standard deviation of the mean. The numbers 81 = 74 + 7 and 67 = 74 – 7 are exactly the values 1 standard deviation above and below the mean. So about 68% of students will score within that interval, 68% >65%.
Finally, (C) is not correct. In a normal distribution, 50% of the data is above the mean and 50% is below the mean. If about 50% of students score above 74, then fewer than 50% of students will score above the higher number, 75. A correct statement might have read, “More than half the students scored above 70.” (Since 70 < 74 = the mean.)
Answer is (A) and (B).
Attachment:
GMAT-Club-Forum-6a62qqvu.png [ 212.41 KiB | Viewed 40 times ]
