Problem Solving

The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?

[spoiler]OA: 98[/spoiler]

The percentages are valid for any question involving a normal distribution, and one should memorize them as 34: 14 : 2. The percentages correspond to the 1st, 2nd, and 3rd standard deviations on each side of the mean. A student scoring 78 on the exam is placed two standard deviations on the right side of the mean, that is 50% (mean) + 34% + 14% = 98%

Hi Pemdas,

Can you give a detailed explanation to the above logic ?

pemdas wrote:The percentages are valid for any question involving a normal distribution, and one should memorize them as 34: 14 : 2. The percentages correspond to the 1st, 2nd, and 3rd standard deviations on each side of the mean. A student scoring 78 on the exam is placed two standard deviations on the right side of the mean, that is 50% (mean) + 34% + 14% = 98%

can you please explain the solution.

Would this even be a GMAT question Since it requires knowledge of the normal distribution and standard deviation's relation in normal distributions?

https://www.regentsprep.org/Regents/math ... Lesson.htm

Standard deviation is not such a big deal as much as mean and median are concerned in GMAT exam. They are all central tendency measures studied at the college level and sometimes included in SAT advanced exam question sets. Why would normal distribution be mentioned here is to validate that the central tendency measures are relevant for their application. There is only one special relation of standard deviation to normal probability related to the pure statistical science and it was not mentioned here, z-score and the table of values for each degree variance.

As such, this is a valid GMAT question and will be tested at the medium to low-average difficulty levels of applied algebra section. There's nothing to be rounded as logic here, but one rule of 34-14-2 to memorize and it was described in my previous post.

jbivins wrote:Would this even be a GMAT question Since it requires knowledge of the normal distribution and standard deviation's relation in normal distributions?

https://www.regentsprep.org/Regents/math ... Lesson.htm

Ian, please check Princeton Review's manual for GMAT exam. It's exclusively for their students, version 8.0 and page # 96. Do you think guys at @PR waste their time and people's moneys teaching the students 34-14-2 stuff?

Ian Stewart wrote:

pemdas wrote:

As such, this is a valid GMAT question and will be tested at the medium to low-average difficulty levels of applied algebra section.

No, this is definitely not a 'valid' GMAT question. Normal distributions are never tested on the GMAT. I've seen quite a few prep company questions about normal distributions and the 68-95-99 rule, and they are all completely irrelevant questions for GMAT test takers to study.