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)?