A certain machine makes electrical resistors having a mean resistance of 40 ohm and a standard deviation of 4 ohms. Assuming that the resistance follows a normal distribution and can be measured to any degree of accuracy, the resistors are acceptable only if fallow the specification which is 30 ohm to 50 ohm. ? (i) What percentage of resistors will go to scrap? (ii) Find the probability that a resister has more than 50 ohm resistance?
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 certain machine makes electrical resistors having a mean resistance of 40 ohm and a standard deviation of 4 ohms. Assuming that the resistance follows a
(i) What percentage of resistors will go to scrap?
(ii) Find the probability that a resister has more than 50 ohm resistance?
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