A study was conducted to examine the relationship between the cost structure

A study was conducted to examine the relationship between the cost structure and the mechanical properties of equiaxed grains in unidirectionally solidified ingots (Metallurgical Transactions, May 1986). Ingots composed of copper alloys were poured into one of three mold types (columnar, mixed, or equiaxed) with either a transverse or a longitudinal orientation. From each ingot, five tensile specimens were obtained at varying distances (10, 35, 60, 85, and 100 millimeters) from the ingot chill face and yield strength was determined.
a. How many strength measurements will be obtained if the experiment includes one ingot for each mold type–orientation combination?
b. Suppose three of the ingots will be selected for further testing at the 100-mm distance. How many samples of three ingots can be selected from the total number of ingots in the experiment?
c. Use Table 6 of Appendix II to randomly select the three ingots for further testing.
d. Calculate the probability that the sample selected includes the three highest tensile strengths among all the ingots in the experiment.
e. Calculate the probability that the sample selected includes at least two of the three ingots with the highest tensile strengths.

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