The manufacturer of a quartz travel alarm clock claims that, on the average, its clocks deviate from perfect time by 30 seconds per month, with a standard deviation of 10 seconds. Engineers from a consumer magazine purchase 40 of the clocks and find that the average clock in the sample deviated from perfect accuracy by 34 seconds in one month.
a. If the manufacturer's claim is correct (i.e., seconds, σ = 10 seconds), what is the probability that the average deviation from perfect accuracy would be 34 seconds or more?
b. Based on your answer to part (a), speculate on the possibility that the manufacturer's claim might not be correct.