Problem Solving

A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68% of the distribution lies within one standard deviation d of the mean, what % of the distribution is less than m+d?

answer: 84%

https://www.echidne-of-the-snakes.com/stats/stnorm3.png

This is based on the above graph for normal distirbution

The blue region is within one SD of mean ..

The light brown (pardon my colour sense) is within 2 SD ..and so on

On either side the blue region denoted m + d ..so the region less that m + d will be the rest 100 - 13.6 + 2.1 = 84 approx

I dont understand this answer.

Is it possible to explain it in another way?

sujaysolanki wrote:https://www.echidne-of-the-snakes.com/stats/stnorm3.png

This is based on the above graph for normal distirbution

The blue region is within one SD of mean ..

The light brown (pardon my colour sense) is within 2 SD ..and so on

On either side the blue region denoted m + d ..so the region less that m + d will be the rest 100 - 13.6 + 2.1 = 84 approx

Perhaps a stupid question... if such a question is asked I assume that a graph must be provided as part of the question stem.

Well the graph is not provided ..if thats what u wanted to know ..and theres nothing too it ..just remember the graph ..and some mental calculation ....although ..it wud be better if GMAC doesnt give such stuff ..but anyways ..

I will try to figure out a diff way to explain

Well I think a graph would be really good here but it is not necessary to solve the question

coz the Q says "large population has a distribution that is symmetric about the mean m."

so 68% is within 1 sd of the mean i.e m+d, m-d =68%

remainig is 32% since the distribution is symmetrical abt the mean hence this 32% would be evenly divided on both the sides of the mean i.e 16% to the right & 16 % to the left

now the 16% to the right is greater than the mean & is also greater than m+d, so this is the portion which is only greater than m+d

hence the reqd % = 100 -16 = 84%

hope this is helpful

Replying to an old thread. The below blog very nicely explains Standard Deviation concept:

https://amarsagoo.blocked/2007/09/m ... ation.html