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.
A probability distribution includes ALL the possible events and must add up to 1. Here you have 50 people, so 50 will be the denominator for each probability ...
P(11 seconds) = 2/50 = 0.04
P(12 seconds) = 5/50 = 0.10
Do this the same for 13, 14, 15, 16 and 17 seconds.
When you are all done, the sum of the 7 probabilities should add up to 1
To determine the probability distribution for the finish times, we need to calculate the probability of each outcome occurring. The probability of an outcome is the number of times that outcome occurs divided by the total number of possible outcomes.
In this case, we know the number of people who finished the race in each time interval. We can use this information to calculate the probability distribution.
Let's calculate the probability for each finish time:
For 11 seconds:
- Number of people who finished in 11 seconds = 2
- Total number of people in the race = 50
- Probability = Number of people who finished in 11 seconds / Total number of people in the race
= 2 / 50
= 0.04
For 12 seconds:
- Number of people who finished in 12 seconds = 5
- Total number of people in the race = 50
- Probability = Number of people who finished in 12 seconds / Total number of people in the race
= 5 / 50
= 0.1
For 13 seconds:
- Number of people who finished in 13 seconds = 8
- Total number of people in the race = 50
- Probability = Number of people who finished in 13 seconds / Total number of people in the race
= 8 / 50
= 0.16
For 14 seconds:
- Number of people who finished in 14 seconds = 10
- Total number of people in the race = 50
- Probability = Number of people who finished in 14 seconds / Total number of people in the race
= 10 / 50
= 0.2
For 15 seconds:
- Number of people who finished in 15 seconds = 21
- Total number of people in the race = 50
- Probability = Number of people who finished in 15 seconds / Total number of people in the race
= 21 / 50
= 0.42
For 16 seconds:
- Number of people who finished in 16 seconds = 2
- Total number of people in the race = 50
- Probability = Number of people who finished in 16 seconds / Total number of people in the race
= 2 / 50
= 0.04
For 17 seconds:
- Number of people who finished in 17 seconds = 2
- Total number of people in the race = 50
- Probability = Number of people who finished in 17 seconds / Total number of people in the race
= 2 / 50
= 0.04
Therefore, the probability distribution for the finish times is:
- For 11 seconds: 0.04
- For 12 seconds: 0.1
- For 13 seconds: 0.16
- For 14 seconds: 0.2
- For 15 seconds: 0.42
- For 16 seconds: 0.04
- For 17 seconds: 0.04