. 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?
Make a frequency distribution of the finish times. Does that approximate a normal, skewed or bimodal distribution?
To find the probability distribution for the finish times, we need to calculate the probability of each finish time occurring.
First, let's determine the total number of people who participated in the race:
Total participants = 2 + 5 + 8 + 10 + 21 + 2 + 2 = 50
Now, we can calculate the probability for each finish time:
Probability of finishing in 11 seconds = Number of people finishing in 11 seconds / Total participants
Probability of finishing in 11 seconds = 2 / 50 = 0.04
Probability of finishing in 12 seconds = Number of people finishing in 12 seconds / Total participants
Probability of finishing in 12 seconds = 5 / 50 = 0.1
Probability of finishing in 13 seconds = Number of people finishing in 13 seconds / Total participants
Probability of finishing in 13 seconds = 8 / 50 = 0.16
Probability of finishing in 14 seconds = Number of people finishing in 14 seconds / Total participants
Probability of finishing in 14 seconds = 10 / 50 = 0.2
Probability of finishing in 15 seconds = Number of people finishing in 15 seconds / Total participants
Probability of finishing in 15 seconds = 21 / 50 = 0.42
Probability of finishing in 16 seconds = Number of people finishing in 16 seconds / Total participants
Probability of finishing in 16 seconds = 2 / 50 = 0.04
Probability of finishing in 17 seconds = Number of people finishing in 17 seconds / Total participants
Probability of finishing in 17 seconds = 2 / 50 = 0.04
Now we have the probability distribution for the finish times:
Finish time (seconds) Probability
11 0.04
12 0.1
13 0.16
14 0.2
15 0.42
16 0.04
17 0.04