Sheets of aluminum from a supplier have a thickness that isnormally distributed with a mean of 50 mm and a standard deviationof 4 mm (call this random variable X). Your company compresses thealuminum with a tool that is normally distributed with a mean of 20mm and a standard deviation of 3 mm (call this random variable Y).You are interested in the random variable V = X – Y, the randomvariable V is the final aluminum thickness. 3.1. What is theprobability that the outputted aluminum (that is, V), will bebetween 25 mm and 32 mm? 3.2. What is the probability that theoutputted aluminum (that is, V), will be between 26.5 mm and 33.5mm? 3.3. If the company had the choice between compressing aluminumto between 25-32 mm or 26.5-33.5 mm, then which is preferred (orneither)? 3.4. In one or two sentences, why is one preferred (ifeither) over the other [continuation of 3.3]; if neither arepreferred, then why?
