Two different running shoe manufacturers market running shoes to first time marathon runners.Swift claims a mean shoe life of 600 km,while Enduramax claims a shoe life of 650 km.If the standard deviation for Swift shoes is 54 km and 124 km for Enduramax,which shoe would you purchase before starting your marathon training (where you figure to run 500 km)? Explain.
A)Enduramax.Enduramax shoes are - $\frac { 75 } { 62 }$ standard deviations from the mean while Swift shoes are - $\frac { 50 } { 27 }$ standard deviations from the mean.
B)Enduramax.The Enduramax shoes have a longer mean shoe life.
C)Swift.Swift shoes are - $\frac { 75 } { 62 }$ standard deviations from the mean while Enduramax shoes are - $\frac { 50 } { 27 }$ standard deviations from the mean.
D)Swift.Swift shoes are - $\frac { 50 } { 27 }$ standard deviations from the mean while Enduramax shoes are - $\frac { 75 } { 62 }$ standard deviations from the mean.
E)Enduramax.Enduramax shoes are - $\frac { 50 } { 27 }$ standard deviations from the mean while Swift shoes are - $\frac { 75 } { 62 }$ standard deviations from the mean.

Question

Quizplus · Accepted Answer

The choice is based on calculating how many standard deviations 500 km (the expected running distance) is from the mean life of each shoe. For Swift, $ \frac{600 - 500}{54} = \frac{100}{54} = \frac{50}{27} $ standard deviations from the mean. For Enduramax, $ \frac{650 - 500}{124} = \frac{150}{124} = \frac{75}{62} $ standard deviations from the mean. Since Swift shoes are closer to their mean life when running 500 km, they are a better choice for this specific training distance.

Two Different Running Shoe Manufacturers Market Running Shoes to First 7562\frac { 75 } { 62 }6275​

Two Different Running Shoe Manufacturers Market Running Shoes to First $\frac { 75 } { 62 }$