# Statistics Question

What percent of observations will lie above the mean plus two standard deviations? (a)5% (b)95% ©2.5% (d)68% The answer is 2.5% but I think it should be 12.5% percent. Don’t know what I am doing wrong? please help…

95% of observations are within ±2 standard deviation. So 5% is not in the range. 2.5% below -2 s.d and 2.5% above +2 s.d.

When I first read the question, I assumed it was a Chebyshev type question as well… so minimum of data would be within 2 SDs would be 75%, so 1/2 of the remaining would be 12.5% as quoted by boilermaker. I’m thinking the assumption here is that it’s a NORMAL distribution and so I think heha168’s line of thinking is in the right direction

iamsmrt, That is exactly what I thought. Since in the question it didn’t say anything about the type of distribution and Chebyshev’s inequality is applicable to any type of distribution. thank you

Each side of the mean contains 50% of the observations. 1.96 stdv (say rounded 2 stdv) around the mean contain 95% of the observations, that’s equivalent to having 47.5% of observations to the right, and 47.5% to the left of the mean. That means, 2.5% remain in the right tail, and 2.5% in th left tail.

map1 Wrote: ------------------------------------------------------- > Each side of the mean contains 50% of the > observations. Not true > 1.96 stdv (say rounded 2 stdv) around the mean > contain 95% of the observations, that’s equivalent > to having 47.5% of observations to the right, and > 47.5% to the left of the mean. That means, 2.5% > remain in the right tail, and 2.5% in th left > tail. for a normal distn but not generally true

iamsmrt Wrote: ------------------------------------------------------- > When I first read the question, I assumed it was a > Chebyshev type question as well… so minimum of > data would be within 2 SDs would be 75%, so 1/2 of > the remaining would be 12.5% as quoted by > boilermaker. I’m thinking the assumption here is > that it’s a NORMAL distribution and so I think > heha168’s line of thinking is in the right > direction Chebyshev says nothing about symmetry and the Chebyshev-like theorem that says that isn’t true