13. Machine components are mass-produced at a factory. A customer requires that the components should be 5.200cm long but they will be acceptable if they are within limits 5.195cm to 5.205cm. The customer tests the components and finds that 11.75% of those supplied are over-size and 5.95% are under-size. Assuming components supplied are normally distributed. What is the probability that one is under-size, one is over-size and one satisfactory given three of the components are selected at random?
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!
What is the probability that one is under-size, one is over-size and one satisfactory given three of the components are selected at random?
In a survey into working practices, the distance walked each day by a postal worker delivering mail in a residential district was recorded. For each weekday (Monday to Friday) the distribution had mean 12km and standard deviation 0.9km. For Saturdays the distribution had mean 10km and standard deviation 0.5km. No mail was delivered on Sundays. The distances walked on different days may be assumed to be independent of each other and normally distributed.
Use this information to answer questions 13-15.
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