At a track meet, 50 people ran the 100-meter dash. 2 people finished in 11 seconds, 5 people finished in 12 seconds, 8 people finished in 13 seconds, 10 people finished in 14 seconds, 21 people finished in 15 seconds, 2 people finished in 16 seconds, and 2 people finished in 17 seconds. What is the probability distribution for the finish times?
Graph it out. What does it look like?
To find the probability distribution for the finish times, we need to calculate the probability of each finish time occurring. First, let's calculate the total number of people who participated in the 100-meter dash, which is 50.
Next, we'll calculate the probability for each finish time. The probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
In this case, the favorable outcome is the number of people who finished the race in a specific time, and the total number of possible outcomes is the total number of people who participated in the race.
For example, the probability of finishing the race in 11 seconds is calculated by dividing the number of people who finished in 11 seconds (2) by the total number of people (50).
The probability distribution for the finish times is as follows:
11 seconds: 2/50 = 0.04 or 4%
12 seconds: 5/50 = 0.1 or 10%
13 seconds: 8/50 = 0.16 or 16%
14 seconds: 10/50 = 0.2 or 20%
15 seconds: 21/50 = 0.42 or 42%
16 seconds: 2/50 = 0.04 or 4%
17 seconds: 2/50 = 0.04 or 4%
Therefore, the probability distribution for the finish times in the 100-meter dash is as follows:
11 seconds: 0.04 or 4%
12 seconds: 0.1 or 10%
13 seconds: 0.16 or 16%
14 seconds: 0.2 or 20%
15 seconds: 0.42 or 42%
16 seconds: 0.04 or 4%
17 seconds: 0.04 or 4%