X is dist Exp(L)

H0: 1/L = 100 , H1: 1/L = 200 Reject H0 if x>460

I have worked out probabilities of making type1 and 2 errors by working out:

Pr(x>460) for L = 1/100 & Pr(x<460) for L = 1/200 giving 0.01005 & 0.89974

Can anyone tell me if this is correct, the second answer seems too high but then it probably is quite likely seeing as x 1/L is only 200 which is a lot smaller than 460