10. The diameters of screws in a batch are normally distributed with mean equal to 2.10 cm and standard deviation equal to 0.15 cm. a) What proportion of screws are expected to have diameters greater than 2.50 cm? b) A specification calls for screw diameters between 1.75 cm and 2.50 cm. What proportion of screws will meet the specification?
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!
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