In: Statistics and Probability
In a certain distribution, the mean is
40
with a standard deviation of
5
At least what fraction of the numbers are between the following pair of numbers?
30
and 50
Solution:
= 40
= 5
According to Chebyshevs's theorem , the minimum probability of
"between
- k
and
+ k
" is 1 - (1/k2)
So , minimum probability of "between
- 2
and
+ 2
" is 1- (1/22 ) i.e. 3/4
"Between 30 and 50 " = "between 40 - (2*5) and 40 + (2*5)" =
"between
- 2
and
+ 2
"
So , answer is 3/4 i.e 0.75
At least 3/4 of the numbers are between the following pair of numbers 30 and 50