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

Question

1. lim n→∞ P(n/3−10≤Sn≤n/3+10)=

2. lim n→∞ P(n/3−n/6≤Sn≤n/3+n/6)=
ans = 1

3. lim as n→∞ P(n/3−√2n/5≤Sn≤n/3+√2n/5)=

Kindly help with question 1 & 3.

Answer 1

1) 0
2) 1
3) 0.4514