(d)(2 pts) Let Y = 10-X. In words, what does Y represent? (e)(2 pts) Use the cdf
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(d)(2 pts) Let Y = 10-X. In words, what does Y represent? (e)(2 pts) Use the cdf to find P(2 SY 5). (Hint: Just plug in Y-10- x) Question 4 (10 points) The resistence for resistors of a certain type is a random variable X having the nor- mal distribution with mean 9 ohms and standard deviation 0.4 ohms. A resistor is acceptable if its resistance is between 8.6 and 9.8 ohms. (a)(5 pts) What is the probability that a randomly chosen resistor is acceptable? (Hint: Check normal table in appendix or use R.) (b)(5 pts) What is the probability that out of four randomly and independently selected resistors, two are acceptable? (Hint: Link this to the interpretation ofa binomial random variable.)Explanation / Answer
4.
Params of normal distribution have been given as mean = 9 and Stvdev is. 4
8.6 is deviation below mean and 9.8 is 2 deviation above mean. Which means the area between 8.6 and 9.8 is.. 34+.475=. 815 or 81.5 percentage of resistors are acceptable.
B. We have pointed out that p =.815 and n=4 from this question.
We find p(x, n, p) = p(2, 4,. 815) = 4C2 *. 815^2 *.185^2 =.1364
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