deviation of 2,250 miles. (Assume the life spans of the tires have a bell-shaped distribution.) (a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 32,000 miles. Find the z-score that corresponds to each life span. For the life span of 34,000 miles, z-score is ___________(Round to the nearest hundredth as needed.) For the life span of 37,000 miles, z-score is _________(Round to the nearest hundredth as needed.) For the life span of 32,0
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 certain brand of automobile tire has a mean life span of 36,000 miles and a standard deviation of 2,250 miles. (Assume the life spans of the tires have a bell-shaped distribution.)
(a) The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 32,000 miles. Find the z-score that corresponds to each life span.
For the life span of 34,000 miles, z-score is ___________(Round to the nearest hundredth as needed.)
For the life span of 37,000 miles, z-score is _________(Round to the nearest hundredth as needed.)
For the life span of 32,000 miles, z-score is ________(Round to the nearest hundredth as needed.)
According to the z-scores, would the life spans of any of these tires be considered unusual?
yes or no? _________
(b) The life spans of three randomly selected tires are 31,500 miles, 40,500 miles, and 36,000 miles. Using the empirical rule, find the percentile that corresponds to each life span.
The life span 31,500 miles corresponds to the ___________th percentile.
The life span 40,500 miles corresponds to the ________th percentile.
The life span 36,000 miles corresponds to the ___________th percentile.
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