need help with this questionThanks！ 2. A company produces wires with mean resistance 1 ohm and standarddeviation 0.03 ohms. A wire is considered good, if its resistance fallsbetween 0.97 and 1.03. An electrical engineer is building a circuit thatneeds 7 of these wires. The engineer purchases 8 wires; the extra oneis to secure the success of the project.(i) What assumption can you make about the distribution of the re-sistance of a wire?(ii) What is the probability that the engineer will be able to build thecircuit?

Name: need help with this questionThanks！ 2. A company produces wires with m
Uploaded: 2024-03-20T07:07:37.000Z
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Description: need help with this questionThanks！ 2. A company produces wires with mean resistance 1 ohm and standarddeviation 0.03 ohms. A wire is considered good, if its resistance fallsbetween 0.97 and 1.03. An electrical engineer is building a circuit thatneed

(i). Here, the necessary assumption is that the resistance of the wire follows a normal distribution. (ii) The mean and standard deviations are given as 1 and 0.03 respectively. The given values of 0.97 and 1.03 are the points of one standard deviation from the mean value. According to the empirical rule, approximately 68.27% of values fall within one standard deviation from the mean value. Therefore, the probability that a randomly selected wire works well is 0.6827.Define the random variable X as the number of wires that are working well. Here, the number of wires chosen (n) is 8 and each of them is independent of the other. Also, there are two possible outcomes (works well or not) and the probability that a randomly selected wire works well (p) is 0.6827. Thus, X follows the binomial distribution. The PMF of the binomial distribution is given by,Here, for n=8 and p=0.6827. If the engineer wants to build a circuit, it is needed that at least 7 wires should work properly. The required probability can be obtained as follows.