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Question 2 (20 marks) A factory produces cylindrical metal bar. The production process can be modeled by normal distribution with mean length of 11 cm and standard deviation of 0.25 cm. (a) What is the probability that a randomly selected cylindrical metal bar has a length longer than 10.5 cm? (6) There is 14% chance that a randomly selected cylindrical metal bar has a length longer than K. What is the value of K? (c) The production cost of a metal bar is $80 per cm plus a basic cost of $100. Find the mean, median, standard deviation, variance, and 864 percentile of the production cost of a metal bar. (d) Write a short paragraph (about 30 - 50 words) to summarize the production cost of a metal bar. (The summary needs to include all summary statistics found in part (c)). (e) In order to minimize the chance of the production cost of a metal bar to be more expensive than $1000, the senior manager decides to adjust the production process of the metal bar. The mean length is fixed and can't be changed while the standard deviation can be adjusted. Should the process standard deviation be adjusted to (I) a higher level than 0.25 cm. or (II) a lower level than 0.25 cm? (Write down your suggestion, no explanation is needed in part (e)).