Question

Let Sn be the number of successes in n independent Bernoulli trials, where the probability of success for each trial is 1/3 . Provide a numerical value, to a precision of 3 decimal places, for each of the following limits.

1. lim P (n/3 - 10 < Sn < n/3 + 10)

2. lim P (n/3 - n/6 < Sn < n/3 + n/6)

3. lim P (n/3 - sqrt(2n)/5 < Sn < n/3 + sqrt(2n)/5)