A production process whose standard deviation is known to be 1.2 cm has been recalibrated. After the latest round of adjustments, those responsible for this process are still unclear as to the mean size of outputs from this process. Suppose a random sample of 35 observations was taken after the latest adjustment and exhibited a sample mean of 100.65 cm.

(a) Which distribution can we use to construct a confidence interval for the true mean of this process?

• A. The sample is random, the population size is 35, which is large enough, and the population standard deviation is known. Therefore, we can use normal distribution (z-score)

• B. The sample is random, but we do not know the distribution of the original population. Therefore, though the sample size is larger than 30, we have to use Student's t distribution (t-statistic)

• C. We are interested in the population proportion. The sample is random, and it is large enough (n = 30). Therefore, we should use normal distribution (z-score)

• D. Neither the normal distribution nor t-distribution assumptions are satisfied. Therefore, we do not know how to construct the confidence interval in this case (at least based on what we learned in this class)

(b1)-lower What would a 99% confidence interval for the true mean of the production process would be? Express your answer in cm, round your answer to at least two decimals. Enter the lower limit for the confidence interval below:

(b2)-upper What would a 99% confidence interval for the true mean of the production process would be? Express your answer in cm, round your answer to at least two decimals. Enter the upper limit for the confidence interval below:

(c) The recalibration intended to achieve a mean length of 100 cm. Based on the confidence interval that you constructed in part a., do you think that the process was recalibrated properly? Explain your answer.