Suppose the service time in minutes at a bank has the exponential distribution with lambda = 1/2. Use the central limit theorem to estimate the probability that the average service time of the first n customers is less than 2.5 minutes.
a)n=16
b)n=36
c)n=100
My attempt
E(X)=2
Var(X)=4
a)
P(sampleX[16] <= 2.5)
P( [sampleX[16] - 2] / sqrt(1/4) <= [2.5 - 2] /sqrt(1/4) )
P(X<= 1) where x~N(0,1)
Is this right for a)?