In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. It is known that 77% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 64 new products, find the following probabilities. (Round your answers to four decimal places.) n USE SALT (a) within 2 years 47 or more fail 0.8968 (b) within 2 years 58 or fewer fail 0.9877 (c) within 2 years 15 or more succeed 0.5788 (d) within 2 years fewer than 10 succeed 0.0483
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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