Refer to the Baseball 2008 data, which reports information on the 30 Major League Baseball teams for the 2008 season. Set up a variable that divides the teams into two groups, those that had a winning season and those that did not. That is, create a variable to count the teams that won 81 games or more, and those that won 80 or less. Next create a new variable for attendance, using three categories: attendance less than 2.0 million, attendance of 2,0 million up to 3.0 million, and attendance of 3.0 million or more.
a. Create a table that shows the number of teams with a winning season versus those with a losing season by the three categories of attendance. If a team is selected at random, compute the following probabilities:
1. Having a winning season.
2. Having a winning season or attendance of more than 3.0 million.
3. Given attendance of more than 3.0 million, having a winning season.
4. Having a losing season and drawing less than 2.0 million.
b. Create a table that shows the number of teams that play on artificial surfaces and natural surfaces by winning and losing records. If a team is selected at random, compute the following probabilities:
1. Selecting a team with a home field that has a natural surface.
2. Is the likelihood of selecting a team with a winning record larger for teams with natural or artificial surfaces?
3. Having a winning record or playing on an artificial surface.
Answer:
Step 1 of 2:
(a)
We are asked to create a table that shows the number of teams with a winning season versus those with a losing season by the three categories of attendance.
From the given data we can create a table that shows the number of teams with a winning season versus those with a losing season by the three categories of attendance.
Team Result |
Attendance (in million) |
|||
Total |
||||
Winning |
6 |
8 |
4 |
18 |
Losing |
5 |
6 |
1 |
12 |
Total |
11 |
14 |
5 |
30 |
If a team is selected at random, compute the following probabilities:
- Having a winning season.
From the above table, we can see that the team has won total 18 games out of 30.
The probability
-
Having a winning season or attendance of more than
million.
We need to find
Using addition theorem of probability, we can write,
From the table, we can find the numbers,
-
Given attendance of more than
million, having a winning season.
We need to find
We know the conditional probability,
Hence we can write from the table,
- Having a losing season and drawing less than 2.0 million.
We need to find
We can write from the table,