Let Sn be the number of successes in n independent Bernoulli trials, where the probability of success for each trial is 1/2. 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

limn→∞P(n2−20≤Sn≤n2+20)=- unanswered
limn→∞P(n2−n3≤Sn≤n2+n3)=- unanswered
limn→∞P(n2−n−−√4≤Sn≤n2+n−−√4)=

Answer 1

0
1
0.383

Answer 2

Part 3 is wrong.
When you take the limits, it goes to -3/5 < Z < 3/5
So you calculate the difference on the normal table (.7257 - (1-.7257)) = (.7257 - .2743) = .4514