Suppose the area that can be painted using a single can of spray paint is slightly variable and follows a nearly normal distribution with a mean of 29 square feet and a standard deviation of 3 square feet. (a) What is the probability that the area covered by a can of spray paint is more than 31 square feet? (Round your answer to four decimal places.) (b) Suppose you want to spray paint an area of 310 square feet using 10 cans of spray paint. On average, how many square feet must each can be able to cover to spray paint all 310 square feet? (Enter your answer as a whole number.) (c) What is the probability that you can cover a 310 square feet area using 10 cans of spray paint? (Round your answer to four decimal places.)
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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