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24 Feb 2014, 18:36
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
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Question Stats:
77% (01:09) correct
23%
(01:28)
wrong
based on 48
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I encountered this question an a Princeton Review practice test. I can see why both statements are necessary, but I don't really understand the underlying explanation. I don't understand how they got the ratio of 1,2,3 standard deviations from the mean.
At a golf driving range, a computer automatically records the length of each drive. The distribution of drive lengths follows a normal distribution. Is the percentage of drives over 200 feet in length greater than 15%?
(1) The average drive length is 150 feet.
(2) The standard deviation is 50.
The explanation given was:
The question states that the drive lengths follow a normal distribution, which means that ratio of items within 1, 2, and 3 standard deviations from the mean is 34:14:2. Statement (1) tells us the mean (average), but does not indicate the standard deviation. Statement (1) is not sufficient. Eliminate AD. Statement (2) gives the standard deviation, but not the mean. Statement (2) is not sufficient. Eliminate B. Taken together, Statements (1) and (2) provide the mean and the standard deviation, so we can calculate what percentage of drives are over 200 feet in length. If the mean is 150 and the standard deviation is 50, then 34% of the drives are between 150 and 200 feet, 14% are between 200 and 250, and 2% are between 250 and 300. Thus, 16% of the drives are over 200 feet in length, and the answer to our question is YES, the percentage of drives over 200 feet in length is greater than 15%. Statements (1) and (2) together are sufficient. Eliminate E. The correct answer is C
At a golf driving range, a computer automatically records the length of each drive. The distribution of drive lengths follows a normal distribution. Is the percentage of drives over 200 feet in length greater than 15%?
(1) The average drive length is 150 feet.
(2) The standard deviation is 50.
The explanation given was:
The question states that the drive lengths follow a normal distribution, which means that ratio of items within 1, 2, and 3 standard deviations from the mean is 34:14:2. Statement (1) tells us the mean (average), but does not indicate the standard deviation. Statement (1) is not sufficient. Eliminate AD. Statement (2) gives the standard deviation, but not the mean. Statement (2) is not sufficient. Eliminate B. Taken together, Statements (1) and (2) provide the mean and the standard deviation, so we can calculate what percentage of drives are over 200 feet in length. If the mean is 150 and the standard deviation is 50, then 34% of the drives are between 150 and 200 feet, 14% are between 200 and 250, and 2% are between 250 and 300. Thus, 16% of the drives are over 200 feet in length, and the answer to our question is YES, the percentage of drives over 200 feet in length is greater than 15%. Statements (1) and (2) together are sufficient. Eliminate E. The correct answer is C
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24 Feb 2014, 20:36
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amy888
Explanation provided is poor. Let me help you with this..
this is a property of normal distribution.
Area under normal distribution between 1 std deviation both side of mean = 68.27% [On one side of mean = 34.13%]
Area under normal distribution between 2 std deviation both side of mean = 65.45% [Difference from above = 27.18%, or on one side of mean = 13.59%]
Area under normal distribution between 3 std deviation both side of mean = 99.73% [Difference from above = 4.28%, or on one side of mean = 2.14%]
These numbers have been rounded and given as 2, 14, 34 in the explanation.
Hope it helps.
24 Feb 2014, 23:27
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amy888
68.2-95.4-99.7 rule of normal distributions is not tested on GMAT.
This is a poor quality question. Topic locked.
