Check Your Head , Part I Over the last few years , there has been growing concern about the long-term effect of callsion* induced concussions in...

Let's turn our attention back to the random variable D¯ we defined earlier. As we know, D¯ follows a normal distribution with mean E(D¯) and variance Var(D¯), both of which we found above.

• Attachment 1
• Attachment 2
• Attachment 3
• Attachment 4

2. Check Your Head , Part IOver the last few years , there has been growing concern about the long-term effect of callsion*induced concussions in professional sports , particularly football . Specifically , collisions thatresult in a player's head undergoing large rotational accelerations are thought to be the mostdangerous - collisions where a player is struck from the side near the chin , for example . Inresponse to this concern , sports equipment companies are attempting to design helmets thatreduce rotational acceleration by directing the force of impact in directions least likely torotate the head .Mi Ke De , a sports equipment company is developing such a helmet and currently has twoprototypes , Prototype* and Prototype { . The team of engineers who designed the helmetsplan to conduct side impact tests with 25 Prototype* helmets and 25 Prototype {' helmets .using accelerometers to measure the rotational acceleration caused by each impact ( the unitsof rotational acceleration are in kiloradians per second squared , or* ^] . Suppose that thedesigners know the standard deviation of the rotational acceleration far side impacts on Pro-tatype* helmets is or = 1.5brake and the standard deviation of the rotational accelerationfor side impacts on Prototype { helmets is ar - 1.5^`^ . Let ur he the true average rota -tional acceleration for side impacts on Prototype* and let us he the true average rotationalacceleration for side impacts on Prototype {. If the designers find evidence that ux _ MYSpring 2010Stat $0.5Homework !)Thursday , April 25then they will use Prototype {. However , if the designers instead find evidence that MY _ MIXthen they will use Prototype*`Since the researchers have not vet collected any data , we can consider the side- impact test.results to he independent random variables , using $ 1 , $7 . .... {} for the side- impact testresults using Prototype* and * 1 . 12 ..... In for the side- impact test results using Prototype*Y .We can also define * = = = $ 1 + 75 }2 + ... + =_$2{ and }" = = 1 1 + 75 /2 + ... + = $25.( a ) What is FIX! ?( h; What is Vari* ] ?"( C ) What is the distribution of* ? How do we know that ?"( d ) What is EIVY ?( e ) What is Vari> > ?!IF ) What is the distribution of !" ? How do we know that ?"