Question

Two pitchers, Jerry and Louis, want to find out who has the faster pitch when compared to each of their teams. Jerry has a speed of 86 miles per hour, and his team has a mean speed of 93 miles per hour and a standard deviation of 3 miles per hour. Louis has a speed of 84 miles per hour, and his team has a mean of 89 miles per hour and a standard deviation of 3.5 miles per hour. Who has the faster pitch when compared to each of their teams

Answer 1

Louis has faster pitch when compared to each of their teams.

Explanation:

We have two pitchers which we need to compare to each of their teams.

To calculate this, we will approximate the distributions to a normal distribution, and calculate the z-score, to know what proportion of players of their team fall below their score.

For Jerry, he has a speed of 86 and his team has a mean speed of 93 and standard deviation of 3.

We can calculate the z-score for Jerry speed as:

`z=(X-\mu)/(\sigma)=(86-93)/(3)=(-7)/(3)= -2.333`

The proportion of players that are below Jerry speed is approximated by the standard normal distribution:

`p=\Phi(z<-2.333)=0.00982`

For Louis, his speed is 84 and his team has a mean speed of 89 and standard deviation of 3.5.

We can calculate the z-score for Jerry speed as:

`z=(X-\mu)/(\sigma)=(84-89)/(3.5)=(-5)/(3.5)= -1.429`

The proportion of players that are below Louis speed is approximated by the standard normal distribution:

`p=\Phi(z<-1.429)=0.0765`

As the proportion of players of Louis team that are below Louis speed is much bigger than the proportion of players of Jerry's team that are below Jerry speed, we can say that Louis has faster pitch when compared to each of their teams.