Although errors are likely when taking measurements from photographic images, these errors are often very small. For sharp images with negligible distortion, errors in measuring distances are often no longer than 0.0004 inch. Assume that the probability of a serious measurement is 0.05. A series of 150 independent measurements are made. Let X denote the number of serious errors made. (a) In finding the probability of making at least one serious error, is the normal approximation appropriate? If so, approximate the probability using this method. (b) Approximate the probability that at least 3 serious errors will be made.
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!
Although errors are likely when taking measurements from photographic images, these errors are often very small. For sharp images with negligible distortion, errors in measuring distances are often no longer than 0.0004 inch. Assume that the
(a) In finding the probability of making at least one serious error, is the normal approximation appropriate? If so, approximate the probability using this method.
(b) Approximate the probability that at least 3 serious errors will be made.
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