Resistors labeled 100 ohms have true resistance that is between 80 ohms and 120 ohms. Let X be the resistance of a randomly chosen resistor. The probability density function of X is given by f(X)= {(x-80)/800 80
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
a. Resistors labeled 100 ohms have true resistance that is between 80 ohms and 120 ohms. Let X be the resistance of a randomly chosen resistor. The probability density
f(X)= {(x-80)/800 80<x<120
0 otherwise
a.Find the mean resistance.
b.Find the standard deviation of the resistances.
c.Find the cumulative distribution function of the resistances.
d.What proportion of resistors have resistances less than 90 ohms?
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