Only 2% of a large population of 100-ohm gold-band resistors have resistances that exceed 105 ohms. For samples of size 100 from this population, describe the exact sampling distribution of the sample proportion of resistors that have resistances in excess of 105 ohms
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The population proportion of resistors exceeding 105 ohms is p = 0.02 (2%), and the sample size is n = 100. Show more…
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Resistors labeled 100Ω have true resistances that are between 80Ω and 120Ω Let X be the mass of a randomly chosen resistor. The probability density function of X is given by f(x) = { (x - 80) / 800 80 < x < 120; 0 otherwise } a. What proportion of resistors have resistances less than 90 Ω? Let X be random variable denoting the mass of randomly chosen resistor. The pdf of X is given by f(x) = (x - 80) / 800; 80 < x < 120 a) The proportion of resistors that have resistance less than 90?, P(X < 90) P(X < 90) = ∫[80 to 90] f(x)dx = ∫[80 to 90] (x - 80) / 800 dx = [ 1/800 * (x^2 / 2) - 1/10 * x ] evaluated from 80 to 90 = 850 / 800 - 10 / 10 = 17 / 16 - 1 = 1 / 16 Hence, the proportion of resistors that have resistance less than 90?, P(X < 90) = 1/16
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A manufacturer knows from experience that the resistance of resistors he produces is normally distributed with a mean of 100 Ω and a standard deviation of 2 Ω. What percentage of the resistors will have resistance less than 102 Ω? [2 points] More than 106 Ω? [2 points] Between 96 Ω and 102 Ω? [4 points]
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Resistors manufactured by a certain process are labeled as having a resistance of 5 Ω. A sample of 100 resistors is drawn, and 87 of them have resistances between 4.9 and 5.1 Ω. True or false: a. The probability that a resistor has a resistance between 4.9 and 5.1 Ω is 0.87. b. The probability that a resistor has a resistance between 4.9 and 5.1 Ω is likely to be close to 0.87, but not exactly equal to 0.87.
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