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

pls explain.

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.

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

I am not sure if this is the right way to come up with SD like subtracting (5'9 - 5'5)/2. I mean 150/900 is 16.6% which is the portion between 5'7 and 5'9, and why are we assuming that they cannot be beyond the 14% area and be in the 16% area(which is also 2 SDs above the mean), why cant they be in the 16% area instead of being near to the mean

By 2 SD, do you mean that 5'7 must be at 1 SD and 5'9 must be at 2 SD?

If 5'72 is at 1 SD (according to the diagram), shouldnt the SD be more than 2?

OE

As with all Quantitative Comparison questions, you need the two values to be expressed in comparable terms, so think of Quantity A in terms of standard deviations above the mean. Because this is a standard deviation question, you might not be able to calculate the exact number of people who are taller than a certain height, but you should be able to approximate it as a percentage of the total.

The question stem states that the data are normally distributed, which means that about 68% of the heights of those involved in the study fall within 1 standard deviation of the mean. It also means that about 95% of those heights fall within 2 standard deviations of the mean. The question stem also says that 150 of the 900 people surveyed were between 5′ 1′′ and 5′ 3′′.

You don’t know how great one standard deviation is, but you do know that a certain percentage of the total data lies between two points. Assume for a moment that one standard deviation is 2′′ in height. In that case, the people whose heights are between 5′ 1′′ and 5′ 3′′ would fall between 1 and 2 standard deviations below the mean of 5′ 5′′. Half of 68% is 34%, which is the amount of data that falls between the mean and 1 standard deviation below the mean. Half of 95% is 47.5%, which is the amount of data that falls between the mean and 2 standard deviations below the mean. Use this information to calculate the percentage of data that would fall between 1 and 2 standard deviations below the mean: 47.5% − 34% = 13.5%.

However, the actual number of people whose heights fall between 5′ 1′′ and 5′ 3′′ is 150/ 900, or about 16.7%, which is more than 13.5%. Normal distribution means that data points are grouped more densely near the mean than farther away from it. Because more than 13.5% of the data falls between 5′ 1′′ and 5′ 3′′, you know this data selection is closer to the mean than the data selection between 1 and 2 standard deviations below the mean. In other words, you don’t know exactly what the standard deviation is for this data set, but you do know it is greater than 2′′. That means that two standard deviations above the mean will be greater than 5′ 9′′; therefore, there are more people who are taller than 5′ 9′′ than people who are 2 standard deviations above the mean.

Quantity A is greater, and the correct answer is (A).

Note: If you memorize 68%, 95%, 99.7%, and other common numbers for data sets with normal distribution, standard deviation problems will be much easier. For example, if you have memorized that about 13.5% of the data in a normal distribution falls between the 1 and 2 standard deviations below the mean, you don’t need to calculate that number. Also note that you don’t really need to calculate 150/ 900. 13.5% of 1,000 would be 135, and you can see at a glance that 150/ 900 is going to be larger than 135/ 1000.

Let me know if still unclear sir