The new computer your business bought lists a mean time between failures of 1 year, with a standard deviation of 3 months. Eight months after a repair, it breaks down again. Is this surprising (Assume that the times between failures are normally distributed.)
A)This is not unusual.
B) This is unusual.

Question

The new computer your business bought lists a mean time between failures of 1 year, with a standard deviation of 3 months. Eight months after a repair, it breaks down again. Is this surprising  (Assume that the times between failures are normally distributed.)  
A)This is not unusual.
B) This is unusual.

Quizplus · Accepted Answer

The mean time between failures is 1 year, or 12 months. The standard deviation is 3 months. Therefore, the distribution of times between failures is normal with a mean of 12 and a standard deviation of 3.

If the computer had failed exactly at 12 months after purchase, that would not be surprising, as it is the mean time between failures. However, the fact that it failed at only 8 months after a repair implies that it is more likely to break down sooner than expected.

We can calculate how surprising this is by finding the z-score of 8 months in relation to the distribution with a mean of 12 and a standard deviation of 3.

z-score = (x - μ) / σ
z-score = (8 - 12) / 3
z-score = -4/3

Looking at a z-score table, we can see that a z-score of -4/3 corresponds to a probability of only 0.0918 or 9.18%. This means that there is less than a 10% chance that the computer would fail so soon after a repair if it truly had a mean time between failures of 1 year with a standard deviation of 3 months.

Therefore, it can be concluded that this is an unusual occurrence and surprising.

The New Computer Your Business Bought Lists a Mean Time