The mean score in a certain test is 80. If the test scores have a norm

Question

The mean score in a certain test is 80. If the test scores have a normal distribution and the standarad distribution is 7, what percent of examinees score between 66 and 94?

A) 50%
B) 68%
C) 82%
D) 96%
E) 98%

PRI23YA · Answer

let mean=x; Standard dev= d;

d=7 i.e. the difference between each deviation from mean is 7 marks.

x+d= 87 (34%) ; x+2d= 94 (14%) ; x-d= 80(34%) ; x-2d= 73 (14%) ; x=3d=66(2%) ==>> between 66 and 94 i.e. sum= 98%

or you can just eliminate above 94 marks percentage from 100% to get the answer.

bv8562 · Answer

Mean = m
SD = d

Mean = 80
SD = 7

94 = 80+2*7 = m+2d
66 = 80-2*7 = m-2d

Therefore, we need to find the percentage of scores that lie between two standard deviations away from mean.

Total percentage that lie between two standard deviations away from mean  (refer to the attached image)  = 34+34+14+14 = 96% (D)

Alankrita26 · Answer

How did you reach at 34% and 14% figures? Is there any way to calculate these or is it just according to properties of normal distribution ?

saurabhSuresh · Answer

Can someone please tell me how to arrive at these percentages? Is there a property in normal distribution that helps in determining the percentages within the standard deviations?

Bunuel

bv8562 · Answer

Alankrita26 saurabhSuresh Yes, this is the property of Normal Distribution. The distribution is symmetric about the mean—half the values fall below the mean and half above the mean. And these percentages are fixed values that you will have to remember. I have also attached a picture in my above post for reference. In the picture, m=mean and d=standard deviation. If a question asks for values one standard deviation away from the mean then we will have to consider both the instances i.e m+d and m-d, both of them are one standard deviation away from the mean. I hope it helps.

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Posted from my mobile device

kingbucky · Answer

Solving this question, means you need to have an additional information about normal curve distribution, which I think is not being tested in GMAT. But, I think someone can clarify if there is any OG question that tests this ?

arunbhati · Answer

Hi

how we get the values of 34%,14% and 2% in this solution

Bunuel · Answer

Normal distribution and the 68-95-99.7 rule are  not  tested on the GMAT. Archiving the topic.

The mean score in a certain test is 80. If the test scores have a norm

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