CLT

Question

Let Xn be i.i.d. random variables with mean zero and variance σ2. Let Sn=X1+⋯+Xn. Let Φ stand for the standard normal CDF. According to the central limit theorem, and as n→∞, P(Sn≤2σn−−√) converges to Φ(a), where:

a=
unanswered
 
Furthermore,

P(Sn≤0) converges to:
unanswered
(Here, enter the numerical value of the probability.)

Answer 1

1) 2
2) 0.5