Final answer:
Approximately 15.87% of tire treads will last less than 28,000 miles, about 81.85% will last between 26,000 and 32,000 miles, and around 2.28% will last more than 34,000 miles.
Step-by-step explanation:
The mean tread life of a tire is 30,000 miles with a standard deviation of 2,000 miles, and tire tread life is normally distributed.
To find the percentage of tire treads that will last less than 28,000 miles, we determine the z-score for 28,000 miles by subtracting the mean from the value and dividing by the standard deviation: z = (28,000 - 30,000) / 2,000 = -1. Consulting a z-table, we find that approximately 15.87% of tire treads will last less than 28,000 miles.
For the range of 26,000 to 32,000 miles, we calculate two z-scores: For 26,000 miles, z = (26,000 - 30,000) / 2,000 = -2; and for 32,000 miles, z = (32,000 - 30,000) / 2,000 = 1. The percentages corresponding to these z-scores represent the tails; subtract them from 100% to find the percentage in between, which is approximately 81.85% of tire treads.
To find the percentage of tire treads that will last more than 34,000 miles, we calculate the z-score for 34,000 miles: z = (34,000 - 30,000) / 2,000 = 2. The z-table shows a small tail percentage beyond 2 standard deviations above the mean, which is approximately 2.28% of tire treads.