A certain brand of automobile tire has a mean life span of 37,000 miles and a standard deviation of 2,400 miles. (Assume the life spans of the tires have a bell-shape distribution.) (a) Tne ire spans or inree ranaomıy seiectea tires are 33,000 miies, 38,000 miies, ana 32,000 miies. Fina tne z-score tnat corresponas to eacn iure span. For the life span of 33,000 miles, z-score is 1.67 (Round to the nearest hundredth as needed.) For the life span of 38,000 miles, z-score is 0.42 (Round to the nearest hundredth as needed.) For the life span of 32,000 miles, z-score is 2.08 (Round to the nearest hundredth as needed.) According to the z-scores, would the life spans of any of these tires be considered unusual? O Yes O No (b) The life spans of three randomly selected tires are 34,600 miles, 39,400 miles, and 37,000 miles. Using the empirical rule, find the percentile that corresponds to each life span. The life span 34,600 miles corresponds to the th percentile. The life span 39,400 miles corresponds to theth percentile. The life span 37,000 miles corresponds to theth percentile.
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 37,000 miles and a standard deviation of 2,400 (Assume the life spans of the tires have a bell-shaped distribution.)
(a) The life spans of three randomly selected tires are 33,000 miles, 38,000 miles, and 32,000 miles. Find the z-score that corresponds to each life span.
For the life span of 33,000miles, z-score is [1.67]
(Round to the nearest hundredth as needed.)
For the life span of 38,000miles, z-score is [0.42 ]
(Round to the nearest hundredth as needed.)
For the life span of 32,000miles, z-score is [2.08 ]
(Round to the nearest hundredth as needed.)
Since we have the answer above, the question is;
According to the z-scores, would the life spans of any of these tires be considered unusual?
Yes or No.
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