teekayy wrote:Students are taking their test, and those who score in the bottom 16 percent will have to retest. If the scores are normally distributed and the mean is 72, what is the score at or below which the students have to retest?

(1) there are 500 students in the class
(2) 10 students scored 82 or higher

answer: C

The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. Each member of the family may be defined by two parameters, location and scale: the mean ("average", μ) and variance (standard deviation squared, σ2) respectively. The standard normal distribution is the normal distribution with a mean of zero and a variance of one (the red curves in the plots to the right). Carl Friedrich Gauss became associated with this set of distributions when he analyzed astronomical data using them,[1] and defined the equation of its probability density function. It is often called the bell curve because the graph of its probability density resembles a bell.

This question needs some background information. Whenever you see 16%, you always remember Gaussian

Statement 1) Just gives us the sample size - Insuf
Statement 2) 10 students scored 82 or higher - Insuf - We need to know how many more students we have

1&2

Min - 10 Students - 62 - 240 students MEAN (72) - 240 students - 82 -1o students - Max

You can find the bottom 16 %, but again this is a MATH question, not a GMAT question.

If anybody knows a GMAT solution, I really want to learn otherwise, I can bore you with calculations:

Please refer to:

https://en.wikipedia.org/wiki/Normal_distribution

In a normal dist..there are three standard deviations to the right and left of the mean. The right first sd comprises 34%, second 14% and third 2% and the same for the left totally to 100%.

Here mean is 72.

ST1 gives us only the total no of students insuff

ST2 gives us the info on 10 students insuff

We need the total and the info on some students.

1+2

Total students 500..10 students score 82+..10 students comprise 2% of 500 so that is the third sd to the right. Hence the diff of 82 and 72 is 10 with 2 sd between them so the SD IS 5..

Bottom 16% is the score from the second sd to the left..so 2 sd below the mean ie 68..which is the failing score.
ans c

jayjk78 wrote:In a normal dist..there are three standard deviations to the right and left of the mean. The right first sd comprises 34%, second 14% and third 2% and the same for the left totally to 100%.

Here mean is 72.

ST1 gives us only the total no of students insuff

ST2 gives us the info on 10 students insuff

We need the total and the info on some students.

1+2

Total students 500..10 students score 82+..10 students comprise 2% of 500 so that is the third sd to the right. Hence the diff of 82 and 72 is 10 with 2 sd between them so the SD IS 5..

Bottom 16% is the score from the second sd to the left..so 2 sd below the mean ie 68..which is the failing score.
ans c

But again, I don't think GMAC wants people to know that 2% is the 3rd SD...

I wonder whether this problem can be solved by regular people with no statistic background..