Question: [22 points] A manufacturer general manager claims that his brand of DVD player has an average life expectancy of 6 years and 6 months with a standard deviation of 1 year and 3 months. Assume that the life expectancy is normally distributed.

(a) [3 points] Randomly selecting one DVD player from this brand, calculate the probability of its life expectancy exceeding 9 years. i.e., find Pr (Y>9)?

(b) [5 points] Again, if randomly selecting one DVD player from this brand, calculate the probability of its life expectancy between 6 and 8 years. i.e., find Pr (6< Y < 8) ?

(c) [4 points]A Consumer magazine decides to test 100 DVDs of this brand. The average life in this sample is 5 years and the sample standard deviation is 2 years. Calculate a 95% confidence interval for the average life (in years).

(d) [5 points] Continue part (c), if a Consumer magazine examine only 25 DVD players and then test the null hypothesis that the mean of these 25 DVDs is 4.5 at the 95% level of significance using a two-tailed test, being sure to write down the null and alternative hypotheses, the test statistic, indicate the rejection region, and provide a conclusion.

(e) [5 points] Repeat part (d), but now test the alternative hypothesis that the mean number of inches is greater than 4.5 at the 95% level of significance using a one-tailed test.