X1, . . . ,Xn are independent and identically distributed random variables?

Question

X1, . . . ,Xn are independent and identically distributed random variables
each with an exponential distribution mean 4. If n = 50 find an
approximation to the probability that the sample mean ¯X is
(a) greater than 4.3,
(b) less than or equal to 3.7.

Answer 1

since N is sufficiently large, you can use a normal approximation.

E(X) is a good approximation for xbar and Var(X)/n is a good approximation for the Variance..

So now: E(X) = 4, V(X) = 16/50 => std. dev. = 4/sqrt(50)

then do it like a standard normal...