A brand of automobile tire has a life expectancy that is normally distributed, with a mean life of 40,000 miles and a standard deviation of 2,500 miles. The lifespan of three randomly selected tires are 35,000 miles, 40,000 miles, and 45,000 miles. Find the z-score that corresponds to each lifespan. Then find the probability of attaining a value larger than (positive z-scores) or smaller (negative z-scores) than the original lifespan. Hint: What is the proportion remaining in the tail for each z-score?
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 brand of automobile tire has a life expectancy that is
The lifespan of a species of fruit fly is normally distributed with a mean of 36 days and a standard deviation of 4 days. The lifespan of three randomly selected flies are 28 days, 34 days, 36 days, and 42 days. Find the z-score that corresponds to each lifespan. Then find the probability of attaining a value larger than (positive z-scores) or smaller (negative z-scores) than the original lifespan.
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