00:01
Okay, so for part eight, the probability of tires wearing out before 20 ,000 miles, well, given that a tire follows a normal distribution, we have that our mean mu of 26 ,000 miles, our standard deviation of 5 ,000, so we have that mu is equal to 26 ,000 miles, we have our standard deviation sigma is going to be 5 ,000 miles, and then we want to find the probability that a tire lasts less than 20 ,000 miles, so this is using the cumulative distribution function or the cdf, so the probability that x is less than 20 ,000, the probability that x is less than 20 ,000 is going to be equal to the cdf of where mu and sigma is equal, and this calculation is approximately equal to 0 .1151, which is going to be about 11 .51%.
01:05
Now, for part b, the probability here of a profit, if they don't have to replace the tires, which happens when tires last more than 20 ,000 miles, so the probability of making a profit on one set of tires, probability of a profit, is equal to 1 minus the probability that x is less than 20 ,000, so that's just equal to 1 minus 0 .1151, which is going to be approximately 0 .8849, so that's going to be 88 .49%...