Ten Corporation makes automobile engines. The life (period before which an engine does no need a major repair) of Model V12 of an engine manufactured by this corporation has a normal distribution with a mean of 10 years and a standard deviation of 2 years.
Find the probability that a randomly selected Model V12 engine lasts more than 12 years before a major repair.
The company is to determine the warranty period for this engine. Any engine that will need a major repair during this warranty will be replaced free by the company. What should the warranty period be if the company does not want to replace more than 1% of the engines?
When four engines are randomly selected, find the probability that the mean life (period before which an engine does no need a major repair) of these four engines is more than 12 years.
When four engines are randomly selected, find the probability that there are exactly two engines which last more than 12 years before a major repair.