Question

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

Answer 1

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