When determining the tensile strength of a certain type of steel, a series of test loads were performed. The breaking point, i.e. the voltage when the steel is missing, was noted and the measurement results (in MPa) are shown in the table below.

(a) Classify the data material (with equally wide classes) and present the result by drawing a histogram. A proposal for class division is, e.g. classes of the form 840-860, etc.

(b) Use the class division from sub-task (a) to calculate the mean and the standard deviation for the data material (i.e. class center with corresponding frequency is used).

(c) Calculate the mean and standard deviation of the original data material and compare with the result in sub-task (b).

(d) Now consider the values as observations of a stochastic variable X that is N(, ), as the value of is estimated with the standard deviation from sub-task (b). Construct a confidence interval for (i.e. the average tensile strength) with a confidence level of 95%.

Table:

918.4 923.9 928.1 932.2 842.6 856.4 857.0 866.0 870.8 872.2 872.2 877.0 877.7 879.1 881.9 886.7 888.1 889.5 890.8 892.2 893.6 897.7 899.1 901.9 905.3 906.0 906.0 906.7 907.4 907.4 908.8 908.8 912.2 912.9 912.9 913.6 913.6 913.6 913.6 914.3 915.0 916.3 917.0 917.7 917.7 917.7 917.7 918.4 918.4 919.1 919.1 920.5 920.5 920.5 922.6 923.2 923.9 923.9 923.9 924.6 925.3 926.0 926.7 926.7 928.8 928.8 928.8 929.4 929.4 929.4 930.1 930.1 932.2 932.2 932.9 932.9 933.6 934.3 934.3 935.7 936.3 936.3 936.3 936.3 936.3 937.0 937.0 937.0 937.0 937.7 937.7 938.4 939.1 939.1 939.8 940.5 940.5 941.9 943.2 943.9 943.9 944.6 945.3 946.0 948.8 948.8 950.1 950.1 950.1 950.8 950.8 952.9 952.9 953.6 953.6 954.3 954.3 954.3 955.0 955.0 955.6 956.3 956.3 958.4 959.1 961.9 962.5 963.9 963.9 965.3 965.3 970.1 971.5 971.5 973.6 975.0 975.6 976.3 985.3 988.7 989.4 990.1 991.5 991.5 992.2 993.6 996.3 996.3 1018.4 1018.4 935.0 935.0 970.1 In addition to adapting the units, the data material is based on the scientific article: D. McLellan and M. McLellan, "Establishing Mechanical Property Allowables for Metals", Journal of Testing and Evaluation 26, no. 3 (1998): 293-299. 918.4 923.9 928.1 932.2 842.6 856.4 857.0 866.0 870.8 872.2 872.2 877.0 877.7 879.1 881.9 886.7 888.1 889.5 890.8 892.2 893.6 897.7 899.1 901.9 905.3 906.0 906.0 906.7 907.4 907.4 908.8 908.8 912.2 912.9 912.9 913.6 913.6 913.6 913.6 914.3 915.0 916.3 917.0 917.7 917.7 917.7 917.7 918.4 918.4 919.1 919.1 920.5 920.5 920.5 922.6 923.2 923.9 923.9 923.9 924.6 925.3 926.0 926.7 926.7 928.8 928.8 928.8 929.4 929.4 929.4 930.1 930.1 932.2 932.2 932.9 932.9 933.6 934.3 934.3 935.7 936.3 936.3 936.3 936.3 936.3 937.0 937.0 937.0 937.0 937.7 937.7 938.4 939.1 939.1 939.8 940.5 940.5 941.9 943.2 943.9 943.9 944.6 945.3 946.0 948.8 948.8 950.1 950.1 950.1 950.8 950.8 952.9 952.9 953.6 953.6 954.3 954.3 954.3 955.0 955.0 955.6 956.3 956.3 958.4 959.1 961.9 962.5 963.9 963.9 965.3 965.3 970.1 971.5 971.5 973.6 975.0 975.6 976.3 985.3 988.7 989.4 990.1 991.5 991.5 992.2 993.6 996.3 996.3 1018.4 1018.4 935.0 935.0 970.1 In addition to adapting the units, the data material is based on the scientific article: D. McLellan and M. McLellan, "Establishing Mechanical Property Allowables for Metals", Journal of Testing and Evaluation 26, no. 3 (1998): 293-299