In problems 1012 assume that the SkidMore tire company manuf

In problems 10-12. assume that the Skid-More tire company manufactures tires that have a tire-life which is normally distributed with a mean lifetime of 22,000 miles and a standard deviation of 1,500 miles. 10. If 16 Skid-More tires are selected at random and then tested, find the probability that the mean tire-life of the sample will be less than 21,000 miles. Use Table 1. 12. An inspector from the FTC is assigned to study the durability claims of Skid-More tires. She will take a random sample of 25 tires for testing. If the mean tire-life of the 25 tires in the sample is less than 21,250 miles, then Skid-More will be subject to federal fraud penalties. Find the probability that this will happen. Use Table 1.

Solution

(10) P(xbar<21000) = P((xbar-mean)/(s/vn) <(21000-22000)/(1500/sqrt(16)))

=P(Z<-2.67) =0.0038 (from standard normal table)

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(12)P(xbar<21250) = P(Z<(21250-22000)/(1500/sqrt(25)))

=P(Z<-2.5) = 0.0062(from standard normal table)