The members of the newest recruiting class of a certain...

[nehag84]

The members of the newest recruiting class of a certain military organization are taking their physical conditioning test, and those who score in the bottom 16% will have to take a retest. If the scores are normally distributed and have an arithmetic mean of 72, what is the score at or below which the recruits will have to take the retest?

1) There are 500 recruits in the class
2) 10 recruits scored 82 or higher

OA is C.

This Q is in the Princeton Review. I marked E as the answer. Can somebody pls solve it...

[jayachandran.b]

Since this is a normal distribution we can draw the graph with the combined data (72 will come in the middle with max distribution, after 82 there are just 10 people, and before 62 there will be just 10 people, the rest will be normally distributed between 62 and 82 with peak at 72.). And from the graph we can find out any cutoffs.. Of course we don't have to calculate the value, but once you have the image of that graph in mind with the given data you know Albert Einstein can find it out and if he can so can anyone else and thus C.

[Ben Ku]

A normal distribution is a bell curve, that means it's exactly symmetrical. It also has a particular characteristic that is related to the standard deviation of the distribution (e.g. about 68% of the data fall within 1 standard deviation of the mean).

The question is asking for the score that corresponds to the bottom 16% We need to know information about the spread (so we need to find out the number of people scored within a particular range of scores).

(1) We know 500 recruits are in the class, so the bottom 16% represents the bottom 80 recruits. However, this gives us no information about what score this corresponds to.

(2) Knowing 10 recruits scored 82 or higher, we know that 10 recruits scored 62 or lower, since this is a normal distribution. However, we don't know what percentage of the class corresponds to 10 recruits.

(1) and (2) Together: Using the statements together, we know that 10 recruits corresponds to 2% of the class. Because (2) gives us information about the spread and (1) gives us information about the number of students, it is possible (though the computation might be complex) to find the score that represents the bottom 16% or 80 recruits. The answer is (C).

[nehag84]

Thank You!

I just hope this is not representative of the actual tough Qs on GMAT! :-)

[Ben Ku]

I'm glad that helped.

Although the GMAT will never ask you to calculate the standard deviation, you should have a conceptual understanding of what it represents. You might want to refer in the OG 12th Edition to D31 and DS-134 to see how standard deviation is tested.

[tanvi_agt]

Could anyone please explain what is meant by normally distributed?
Is it just another meaning for "evenly distributed"?

[RonPurewal]

Could anyone please explain what is meant by normally distributed?
Is it just another meaning for "evenly distributed"?

It's not. The "normal distribution" (also known as "bell curve") is a very specific statistical distribution, with lots of special properties.

On the GMAT, though, you don't need this sort of outside knowledge. This is a bad question, since it requires knowledge that the GMAT absolutely will not require.

When the GMAT has tested normal distributions, the ONLY fact required has been the symmetry of the distribution (which will usually be mentioned anyway).
So, if you're given some fact like "10% of the population was below X value", then it's reasonable for you to find the value above which 10% of the population is found (= same distance on other side of the mean). Or that 40% of the population lies between X value and the mean. Etc.

Nothing like what's here, though.