Question

5.00 points Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made a study of the maintenance costs and determined the number of miles traveled during the year followed the normal distribution. The mean of the distribution was 60,000 miles and the standard deviation 2,000 miles. (Round z- score computation to 2 decimal places and your final answer to 2 decimal places.) eWhat percent of the Ford Super Duty F-750s logged 65,200 miles or more? Percent What percent of the trucks logged more than 57,060 but less o than 58,280 miles? Percent What percent of the Fords traveled 62,000 miles or less during the year? Percent

Answer 1

Given Mean $\mu =60,000$ and Standard deviation $\sigma =2,000$

a) $Z=\frac{X-\mu }{\sigma }=\frac{65,200-60,000}{2,000}=\frac{5,200}{2,000}=2.6$

$P(X\geq 65,200)=P(Z\geq 2.6)=0.0047$

b) $Z_{1}=\frac{X_{1}-\mu }{\sigma }=\frac{57,060-60,000}{2,000}=\frac{-2,940}{2,000}=-1.47$

$Z_{2}=\frac{X_{2}-\mu }{\sigma }=\frac{58,280-60,000}{2,000}=\frac{-1,720}{2,000}=-0.86$

c) $Z=\frac{X-\mu }{\sigma }=\frac{62,000-60,000}{2,000}=\frac{2,000}{2,000}=1$

$P(Z\leq 62,000)=P(Z\leq 1)=0.8413$