The intake valve clearances on new engines of a certain type are normally distributed with mean 200 μm and standard deviation 10 μm. a) What is the probability that the clearance is greater than 215μm? b) What is the probability that the clearance is between 180 and 205 μm? c) An engine has six intake valves. What is the probability that exactly two of them have clearances greater than 215 μm?
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!
The intake valve clearances on new engines of a certain type are
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