(5 =sprenne 11 The masses of a sample batch of 50 castings produced by two different machines in a company are recorded below, correct in size to the nearest 0.1 kg. Read this question thoroughly before attempting it so you can plan your methods and approach. Machine A \f(a) You are required to draw two tally/frequency tables of 5 or 6 different classes with at least one class being a different width to the other 4 (or 5) for each sample set of results above. You can use the same width intervals for each table (samples from each machme) Use a separate sheet of paper for this task. (b) Draw on 2mm graph paper a histogram for each set of data. Remember, one of your class widths is a different size to the others in your tables so at least one bar in your histograms will have a different width to the others. Frequency densities need to be shown in the tables produced 1n (a). (c) Comment on the symmetry or skewness of each set of sample data and demde giving reasons, if each approximates to a Normal distribution. Explain what a Normal distribution is in a way that a non-mathematician would understand. (d) Calculate the mean and standard deviation for each sample, remembering to use the correct formula for sample data. It may be useful to create enough columns in your tables from (b) above to aid you in showing your methods (clearly) in completing this task. Your working can be completed on the separate piece of paper used for part (a) above. Set out your final answers after showing your working as below: Machine A mean u (or X) = standard deviation o (or Sa) = Machine B mean u (or X) = standard deviation o (or SB) = (e) Compare your results so far and, giving a description for the non- _mathematician of why the means and standard deviations are useful here, decide if one machine 1S more reliable than the other (at the present time) in the production of castings. Remember, the differences n your results can sometimes not be so significant and therefore leave you to conclude that there is little difference in production reliability. (f) The company advertises to its customers that the mean mass is X = 7kg with a 99.7% tolerance of 0.6kg? With reference to your calculations so far, does this information affect your answer to ()? Show some calculations here within your explanation