Suppose that a fair 6sided die is rolled over and over again

Suppose that a fair 6-sided die is rolled over and over again. You may assume that the outcomes for each roll are independent (but identically distributed) from the other rolls. Use Chebyshev\'s inequality to determine the minimum number of times the die should be rolled to say that the average of the outcomes falls between 3.4 and 3.6 with a probability of at least 0.95 That is, if Tis the average of the outcomes of the first N rolls, find the minimum value of N that guarantees that P(3.4 X36) 20.95

Solution

First of all ,

E(X) = (Upper Bound + Lower Bound ) / 2

= (3.4 + 3.6) / 2

= 3.5

Formula is ,

E(X) = n*p

=> n = E(X)/p

=> n = 3.5/0.95

=> n = 3.6842 ~ 4 times Answer