I need help with this problem, can you please show me step by step?

17. (15 points) The manager wanted to know the overall quality of a large batch of products. The quality management team selected a sample of 100 items randomly from the whole batch and measured the value of a key index for each item. The mean value of this key index for this sample is 99. The variance of the Whole batch is estimated to be 16. (a) (5 points) Construct a 95% condence level two-tail condence interval for the mean value of the key index of this batch. (b) (5 points) If we want the sampling error to be no greater than 0.5, what is the minimum sample size to achieve this based on the same condence level with part (a)? (c) (5 points) If the mean value of the key index is less than 100, the batch should be rejected. If you are the manager, do you have evidence to reject this batch based on the results of the current sample with signicant level 0.05