Applying torque A machine fastens plastic screwon caps
Chapter , Problem R6.4(choose chapter or problem)
Applying torque A machine fastens plastic screwon caps onto containers of motor oil. If the machine applies more torque than the cap can withstand, the cap will break. Both the torque applied and the strength of the caps vary. The capping-machine torque T follows a Normal distribution with mean 7 inch-pounds and standard deviation 0.9 inch-pounds. The cap strength C (the torque that would break the cap) follows a Normal distribution with mean 10 inch-pounds and standard deviation 1.2 inch- pounds. (a) Explain why it is reasonable to assume that the cap strength and the torque applied by the machine are independent. (b) Let the random variable D = C T. Find its mean and standard deviation. (c) What is the probability that a cap will break while being fastened by the machine? Show your work. Exercises R6.5 and R6.6 refer to the following setting. According to the Mars candy company, 20% of its plain M&Ms candies are orange. Assume that the companys claim is true. Suppose that you reach into a large bag of plain M&Ms (without looking) and pull out 8 candies. Let X = the number of orange candies you get. s Determine whether the conditions for a binomial random variable are met. s Calculate the mean and standard deviation of a binomial random variable. Interpret these values in context.
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