The average life of a certain type of small motor is 10 years with a standard deviation of 2 years. Assume that the lifetime of a motor follows a normal distribution.

a. Calculate the probability that the life of a randomly selected motor is less than 9 years

b. The manufacturer replaces free all motors that fail while under guarantee. If he is willing to replace only 3% of the motors that fail, how long a guarantee should he offer?

c. A random sample of 9 motors is tested by a researcher, and the average life is found to be x = 9 years. Do we have reason to believe that the average life is different than 10 years? Use level of significance = 0.05. Present all the five steps of a HTP!

d. Calculate P -value for the two-sided test.

e. Use the calculated P-value (in Q10, part d. ) and give one example of value for for which you would reject the null hypothesis.