statistics question part b used the CLT

do c,d and e step by step workout with formulas clearly shown. Use the table provided

Question 5 To investigate the actual contents of 600ml bottles of drinking water marketed by a well- known Australian company, a Market Research Team took a randomly selected sample of 36 water bottles of the same brand. The sample mean and standard deviation of the random sample were found to be 598mL and 4.9mL respectively. Assume that the distribution of the content of water in the bottles is normal with mean 600mL and standard deviation 3.5mL. (a) What type of distribution will the sampling distribution of the sample mean be? State its parameters and the values of those parameters in this context. ( b ) Find the probability that the mean of the random sample will exceed 601mL. (C If the population mean and standard deviation were unknown, what would be the 95% confidence interval for the population mean of content of the bottles? (d) Find the probability that the sample mean of a random sample of size 50 from the population will exceed 601ml. (e) mark.) If the Market Research Team wants to halve the margin of error, how many times larger or smaller should the sample size (n) be?Two Talled Lower One Taked Upper One Talled t-distribution Critical Values Two-tail probability 0.20 0.1 0.05 0.02 0.01 One-tail probability 0.10 0.05 0.025 0.01 0.005 df 3.078 6.314 12.706 31.821 63.657 1.886 2.920 4.303 6.965 9.925 1.638 2.353 3.182 4.541 .. ol and on Dog 5.841 4 1.533 2.132 2.776 3.747 4.604 5 1.476 2.015 2.571 3.365 4.032 6 1.440 1.943 2.447 3.143 3.707 7 1.415 1.895 2.365 2.998 3.499 8 1.397 1.860 2.306 2.896 3.355 9 1.383 1.833 2.262 2.821 3.250 10 1.372 1.812 2.228 2.764 3.169 11 1.363 1.796 2.201 2.718 3.106 12 1.356 1.782 2.179 2.681 3.055 13 1.350 1.771 2.160 2.650 3.012 14 1.345 1.761 2.145 2.624 2.977 15 1.341 1.753 2.131 2.602 2.947 16 1.337 1.746 2.120 2.583 2.921 17 1.333 1.740 2.110 2.567 2.898 18 1.330 1.734 2.101 2.552 2.878 19 1.328 1.729 2.093 2.539 2.861 20 1.325 1.725 2.086 2.528 2.845 21 1.323 1.721 2.080 2.518 2.831 22 1.321 1.717 2.074 2.508 2.819 23 1.319 1.714 2.069 2.500 2.807 24 1.318 1.711 2.064 2.492 2.797 8.0 05 25 1.316 1.708 2.060 2.485 2.787 26 1.315 1.706 2.056 2.479 2.779 27 1.314 1.703 2.052 2.473 2.771 28 1.313 1.701 2.048 2.467 2.763 29 1.311 1.699 2.045 2.462 2.756 30 1.310 1.697 2.042 2.457 2.750 35 1.306 1.690 2.030 2.438 2.724 1/ and 40 1.303 1.684 2.021 2.423 2.704 50 1.299 1.676 2.009 2.403 2.678 100 1.290 1.660 1.984 2.364 2.626 500 1.283 1.648 1.965 2.334 2.586 1000 1.282 1.646 1.962 2.330 2.581 1.282 1.645 1.960 2.327 2.576 Confidence levels 80% 90% 95% 98% 99%