If the population variance of the lifetime of a light bulb is 10000 hours, how large of a sample must be taken in order to be 99% confident that the margin of error will not exceed 35 hours

The sample must be greater than 55

Step-by-step explanation:

Confidence = 99% = 0.99

α = 1 - C = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

The z score of α/2 (0.005) corresponds to the z score of 0.495 (0.5 - 0.005) which is equal to 2.576

The margin of error (E) is given by the formula:

n > 55

The sample must be greater than 55 so that the margin of error will not exceed 35 hours