We are given a table that shows the percent of members participating in 4 classes offered at a gym. We want to design and conduct a to estimate the that a new gym member will take each class. First let's review the steps for designing a simulation.
We will follow these steps, then conduct the simulation, and report the results.
Since we are interested in the probability that a new member will take each of 4 classes, we have 4 possible outcomes. Based on the given information, we will assume that the theoretical probability that a new gym member will take each class is the same as the given percentages.
| Possible Outcomes
|
Theoretical Probability
|
Written as Fraction
|
| Tae kwon do
|
45 %
|
9/20
|
| Yoga
|
30 %
|
6/20
|
| Swimming
|
15 %
|
3/20
|
| Kick-boxing
|
10 %
|
2/20
|
Let's use a random number generator to perform the simulation. To do this, because we expressed the probabilities as fractions with denominators of 20, we will assign the integers from 1 to 20 to represent the probability data.
Tae kwon do:& 1,2,3,4,5,6,7,8,9
Yoga:& 10,11,12,13,14,15
Swimming:& 16,17,18
Kick-boxing: & 19,20
Each trial — one generated number — will represent the choice of a new gym member. Let's choose the number of trials to be 20.
Conducting and Summarizing Data from a Simulation
We will use the random number generator in our graphing calculator. To do so, push the MATH button. Then scroll left to the PRB menu and choose the fifth option, randInt(.
After choosing this option, enter the minimum and maximum values of the set, and the number of trials. Next, push ENTER.
Now, we can make a to show the example results of our simulation. Remember the numbers that we assigned to represent each class when keeping track of the outcomes.
| Outcome
|
Tally
|
Frequency
|
| Tae kwon do
|
|||| ||||
|
10
|
| Yoga
|
|||| |
|
6
|
| Swimming
|
|||
|
3
|
| Kick-boxing
|
|
|
1
|
| Total
|
-
|
20
|
Using the results from the table, we can calculate the P of choosing each class. We will divide the frequency of choosing each class by the number of trials, 20.
| Outcome
|
Frequency
|
Probability P
|
| Tae kwon do
|
10
|
10/20 or 50 %
|
| Yoga
|
6
|
6/20 or 30 %
|
| Swimming
|
3
|
3/20 or 15 %
|
| Kick-boxing
|
1
|
1/20 or 5 %
|
Finally, we can create a showing these results.
