k=0.75 A factory manufactures 1000k Ohm electrical resistors. Due to imperfections in the production, the resistors are not exactly 1000k Ohm, but have to be treated as a random variable which we will call X. The probability density function for X is a normal (Gaussian) distribution with mean 1000k and variance 40k. a) What is the probability that the resistance value of a randomly chosen resistor is higher than 1010k Ohms? b) What is the probability that the resistance value of a randomly chosen resistor is between 1020k and 990k Ohms? c) What is the value of c for which there is 88% probability that the resistance value is within the interval [1000k − c, 1000k + c]?
k=0.75
A factory manufactures 1000k Ohm electrical resistors. Due to imperfections in the production, the resistors are not exactly 1000k Ohm, but have to be treated as a random variable which we will call X. The
a) What is the probability that the resistance value of a randomly chosen resistor is higher than 1010k Ohms?
b) What is the probability that the resistance value of a randomly chosen resistor is between 1020k and 990k Ohms?
c) What is the value of c for which there is 88% probability that the resistance value is within the interval [1000k − c, 1000k + c]?
d) Now let’s consider a second factory which also produces 1000k Ohm resistors. Again, due to imperfections in the production, the resistors are not exactly 1000k Ohms, but have to be treated as a random variable which we will call Y. The probability density function for Y is again a
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