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Normal Distribution Problems A constant or DC current source that outputs 1 amp is connected to a resistor of nominal resistance of 1 ohm. If the resistance value can vary according to R ∼ Normal(1, 0.01), what is the probability that the voltage across the resistor will be between 0.9 and 1.1 volts? A random voltage X is input to a full wave rectifier that produces at its output the absolute value of the voltage. Suppose X ∼ Normal(0, σ 2 ). What would σ 2 have to be so that the rectifier has a less than .01 probability of returning an output exceeding 2 volts? 1 Professor Staff always scales his test scores. He adds a number of points c to each score so that 50% of the class get a grade of C. A C is given if the score is between 70 and 80. If the scores have the distribution Normal(65, 38), what should c be? Let X ∼ Normal(µ, σ 2 ). The random variable Y = eX is said to have a log-normal distribution (with the same parameters). Find the p.d.f. of Y and plot it. What might this distribution be good for modeling? 2

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