Problem 167E

Let Y be a random variable with mean 11 and variance 9. Using Tchebysheff’s theorem, find

a a lower bound for P(6 < Y < 16).

b the value of C such that P(|Y − 11| ≥ C) ≤ .09.

Solution

Step 1 of 2

a) We have to lower bound for

Given mean=11

And Variance( =9

=3

By Tchebysheff’s theorem

Here given that

Now And

11-3k=6 and 11+3k=16

By solving above 2 equations we can get the values of ‘k’

Then k=5/3

Now

=1-(9/25)

=16/25

=0.64

Hence the lower bound is 0.64