**Pro-tip**: You may use either R or Python or hand-calculations to answer the computational part of this question, however, you do need to--in any case--explain and justify your answer.

Question 1. An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 800 hours and a standard deviation of 40 hours. A random sample of 16 bulbs will have an average life of less than 775 hours. (15 points)

a) Give a probabilistic result that indicates how rare an event $\bar{X} \leq 775$ is when $\mu= 800$. (Hint: Calculate the probability $P(\bar{X} \le 775)$ when $\mu = 800$). On the other hand, how rare would it be if $\mu$ truly were, say, 760 hours?

Your Answer

b) Please construct a 95% confidence interval on $\mu$ with $\bar{X} = 775$. Is 800 inside the interval?

Your Answer

Question 2. A maker of a certain brand of low-fat cereal bars claims that the average saturated fat content is 0.5 gram. In a random sample of 8 cereal bars of this brand, the saturated fat content was 0.6, 0.7, 0.7, 0.3, 0.4, 0.5, 0.4, and 0.2. *Assume a normal distribution*. (15 points)

a) Please construct a 95% confidence interval on the average saturated fat content.

Your Answer

b) Would you agree with the claim? Justify your answer.

Your Answer