How many more bacteria should you sample to achieve a 0.45-hour margin of error?

Question

You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 40 bacteria reveals a sample mean of 72 hours. The standard deviation is known to be 6.4 hours. You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.45 hours at a 99% level of confidence.

How many more bacteria should you sample to achieve a 0.45-hour margin of error? 

Answer 1

The 99% confidence level corresponds to a the z-score at a probability of 99.5 = 2.58

The sample size (n) = (z-score * standard deviation/margin of error)^2 =

(2.58 * 6.4/0.45)^2 = 1346.4 ~ 1347

So you would need 1347 - 40 = 1317 more bacteria