CLT practice

The random variables Xi are i.i.d. with mean 2 and standard deviation equal to 3. Assume that the Xi are nonnegative. Let Sn=X1+⋯+Xn.

Use the CLT to find good approximations to the following quantities. You may want to refer to the normal table. In parts (a) and (b), give answers with 4 decimal digits.

Normal Table
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a) P(S100≤245)≈
unanswered
b) We let N (a random variable) be the first value of n for which Sn exceeds 119.

P(N>49)≈
unanswered
c) What is the largest possible value of n for which we have P(Sn≤128)≈0.5?

n=
unanswered

1 answer

a) 0.9332
b) 0.8413
c) 64