Question

9. The service life of automobile tires is modeled by a normal curve; the Mean Time Between Failures (MTBF) is 20,000 miles and the standard deviation is 800 miles. Use Table B in Appendix B (page 868 and 869) to solve these problems. a. Determine the probability that a tire will fail before 22,000 miles. (2.5 point) Answer: b. Determine the probability that a tire will last at least 19,000 miles. (2.5 point) Answer: c. The manufacturer wishes to provide a warranty on which he will be obligated to make a replacement of only 1% of the tires sold. For how many miles should he warrant the tires? (2.5 Bonus points) Answer:

Answer 1

Here we have U= 20.000 and os 800 PCX <224000) _X=X4 22,000 -20,000 = 2000 + 2.5 800 800 Plex < 2.5) = 0.5+ Pla<x<2.5) --- 0:5+0:49.38 = 0.8936_ t from Normal Table À PIXY 19,000) _Y X 4 = 19,000–20.000 = 1-1000 = - 128" 800 800 Plz -1°25= 0-5+ PLO<x<1:25) 0.5 + 0.0 0.8944 _ 4 we are given that PexrW = 0.01 _7: X- 20.000 = X csay, 800 P(xxx) = 0.01 * 7o.3 from table] 0.3=_X20.000 800 + 2403 X 20000 - X3 20240 Son 20240 miles he waweant to dieses