Final answer:
Using the Central Limit Theorem, the probability that the mean battery life would differ from the population mean by greater than 16.6 minutes is 0.0171.
Step-by-step explanation:
To solve this problem, we can use the Central Limit Theorem. The distribution for the mean length of time 120 batteries last follows a normal distribution with a mean of 505 minutes and a standard deviation of 86 minutes. To find the probability that the mean battery life would differ from the population mean by greater than 16.6 minutes, we need to calculate the z-score and then find the area under the normal curve beyond that z-score.
Step 1: Calculate the standard error (SE) of the distribution of sample means. SE = standard deviation / square root of sample size. SE = 86 / sqrt(120) = 7.857.
Step 2: Calculate the z-score. z = (sample mean - population mean) / SE. z = (16.6 - 0) / 7.857 = 2.11.
Step 3: Find the area under the normal curve beyond the z-score. Using a standard normal distribution table or calculator, we can find that the area to the right of z = 2.11 is approximately 0.0171.
Therefore, the probability that the mean battery life would differ from the population mean by greater than 16.6 minutes is 0.0171.