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Re: A survey measures the heights of 900 people, which are found [#permalink]
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The question has given that almost 16.67% (150/900) of the people are in between 5.1 and 5.3. But there is no information provided about the standard deviation. But the question has given us the hint about it to check ourselves.

Initially, let's say, the SD is 0.2. Then we can see that 5.1 is -2SD, 5.3 is -1SD. The area between 5.1 and 5.3 should have contained 14% of the data (but which is not because it contains 16.67% as given in question).
Now, let's say, the SD is below 0.2 (like 0.1). Then we can see that, 5.1 is -4SD, 5.3 is -2SD. This area contains very little amount of data which is definitely not 16.67%

But, if we can take the SD above 0.2 (like 0.3), then we can see that 5.1 is -1.33SD and 5.3 is -0.67SD. There is a possibility of containing 16.67% of the data in the range. (the SD is not exactly 0.3, but definitely above 0.2)

So we can plot our necessary info on a bell diagram (normal curve) and see that 2SD is above 5.9 inch. This give our answer that, number of people above 5.9 is larger than the number of people above 2SD.

Answer: Quantity A
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Re: A survey measures the heights of 900 people, which are found [#permalink]
Carcass wrote:
A survey measures the heights of 900 people, which are found to be normally distributed. The mean height is 5′ 5″, and 150 people in the survey have a height between 5′ 1″ and 5′ 3″.

Quantity A
Quantity B
The number of people in the survey who are taller than 5′ 9″
The number of people in the survey who are more than 2 standard deviations above the mean



A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given

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pls explain.
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Re: A survey measures the heights of 900 people, which are found [#permalink]
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150 is 16.67% of 900. If it was exactly 16%, A would have been equal to B. But it is not. That means the S.D. is less than 2". Hence A>B.
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Re: A survey measures the heights of 900 people, which are found [#permalink]
Shouldn't the SD be > 2 in these cases?

This is assuming that the starting point of the population with height > 5"9" would only fall before "2 * SD" would Column A > B

please clarify

thanks
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