the life of a street bulb follows an exponential distribution with a mean time of 3 years, the bulbs are replaced whenever they fail. Out of the 1000 street bulbs in the city what is the probability that at most 250 of them will need to be replaced during the first year?

My approach is to first calculate the cdf for the exponetial distriution, and then use the the normal approx, using the facts that the mean of the random variable is u = np and sigma = sqrt(np*(1-p)). But I get the answear to 0.0099 which feels not right