1.A manufacturer of bolts has aquality-control policy that requires it to destroy any bolts that are more than 2 standard deviations from the mean. Thequality-control engineer knows that the bolts coming off the assembly line have mean length of 12 cm with a standard deviation of 0.10 cm. For what lengths will a bolt bedestroyed?

2.Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2600 grams and a standard deviation of 600 grams while babies born after a gestation period of 40 weeks have a mean weight of 3000 grams and a standard deviation of 475 grams. If a 32-week gestation period baby weighs 2100 grams and a 41-week gestation period baby weighs 2500 grams, find the correspondingz-scores. Which baby weighs less relative to the gestationperiod?

3.In a certaincity, the average20- to29-year old man is 69.8 inchestall, with a standard deviation of 3.1 inches, while the average20- to29-year old woman is 64.1 inchestall, with a standard deviation of 3.8 inches. Who is relativelytaller, a75-inch man or a70-inch woman?

4.The mean finish time for a yearly amateur auto race was 186.06 minutes with a standard deviation of 0.319 minute. The winningcar, driven by Ted, finished in 185.56 minutes. The previousyear's race had a mean finishing time of 111.7 with a standard deviation of 0.129 minute. The winning car thatyear, driven by Kate, finished in 111.41 minutes. Find their respectivez-scores. Who had the more convincingvictory?

ted had a finish time with az-score of ?

kate had a finish time with az-score of ?