Step 1 :Given that the margin of error (E) is 0.7, the standard deviation (s) is 5.2, and the Z-score for a 99% level of confidence is approximately 2.576.
Step 2 :We can use the formula for the sample size (n) which is \(n = (Z * s / E)^2\).
Step 3 :Substitute the given values into the formula: \(n = (2.576 * 5.2 / 0.7)^2\).
Step 4 :Calculate the value of n to get approximately 135.6.
Step 5 :Since we can't have a fraction of a bacterium, we round up to the nearest whole number to get the final sample size.
Step 6 :\(\boxed{n = 136}\)