We appreciate your visit to Chapter 5 Problem 7 Previous Problem Problem List Next Problem 1 point The top selling Red and Vous tire is rated 60000 miles which means. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The probability of the tire wearing out before 60000 miles is about 7.64%, whereas the probability of it lasting more than 73000 miles is approximately 33.36%.
Explanation:
This problem is a good example of how to solve mathematical probability problems pertaining to normally distributed data. Given that the lifespan of the tires is represented by a normal distribution with a mean (μ) of 70000 and a standard deviation (σ) of 7000, we can apply the rules of a standard normal distribution to find the desired probabilities.
A. If we want to find the probability that the tire wears out before 60000 miles, we have to calculate the Z-score for 60000. The Z-score formula is Z = (X - μ) / σ. So, Z = (60000 - 70000) / 7000 = -1.43 approximately. The area ('probability') corresponding to the Z-score -1.43 is 0.0764, meaning there is about a 7.64% chance the tire wears out before 60000 miles.
B. To find the probability that a tire lasts more than 73000 miles, we calculate the Z-score for 73000, i.e., Z = (73000 - 70000) / 7000 = 0.43. The corresponding 'probability' for Z=0.43 is 0.3336, which means the area to the right of it (representing a lifespan greater than 73000 miles) is 1 - 0.3336 = 0.6664 or about a 66.64% chance. However, this result is incorrect. We must note that a Z-score of 0.43 represents the area up to 0.43 (about 0.6664) from the left tail. Thus, the area on the right (representing the lifespan greater than 73000 miles) is 1 - 0.6664 = 0.3336 or 33.36% approximately.
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