Hi! I hope you could help me with this Statistics and Probability problem? Thank you!

Three shifts run continuously at a local drink manufacturing plant. Each shift is expected to meet production goals of cases per hour. If the plant is running at 100% efficiency, each shift can produce 486 cases per hour. At a more realistic rate, it is expected that each shift meet the goal of 340 cases per hour. Below is the data for shift 2 for the month of May. 374 355 349 376 404 362 390 368 350 340 378 359 335 334 382 392 320 372 294 286 383 363 (a) What assumptions must be checked before we can construct a confidence interval? (b) What would be an appropriate point estimate for the true production of shift 2 for May? Defend your position. (c) Calculate a point estimate for the true production for shift 2 for the month of May.(d) Construct a 98% confidence interval for the true production for shift 2 for the month of May. (e) The margin of error for this confidence interval is too wide for the production annalists to work with. They need a 98% confidence interval with the error held to a maximum of 10 cases per hour. What size sample is needed to estimate the mean this accurately