A tire manufacturer warranties its tires to last at least 20219 miles or “you get a new set of tires.” In its experience, a set of these tires lasts on average 26219 miles with standard deviation 5146 miles. Assume that the wear is normally distributed. The manufacturer profits Rs. 200 on each set sold, and replacing a set costs the manufacturer Rs. 400. What is the probability that a set of tires wears out before 20219 miles? What is the probability that a set of tires wears out before 2
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!
A tire manufacturer warranties its tires to last at least 20219 miles or “you get a new set of tires.” In its experience, a set of these tires lasts on average 26219 miles with standard deviation 5146 miles. Assume that the wear is
- What is the
probability that a set of tires wears out before 20219 miles? - What is the probability that a set of tires wears out before 24219 miles and after 20219 miles?
- What is the cutoff value in terms of miles of the top 73% wearing out tires.
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