An oil change company advertises that they can change the oil in your car in 15 minutes. Based on the data collected below, what is the probability that oil change will take more than 15 minutes? Using this example as a template, post a similar example from your experience.
Class Interval
Frequency
6 to 10 minutes
3
11 to 15 minutes
8
16 to 20 minutes
6
21 to 25 minutes
2
More than 25 Minutes
1
To find the probability that an oil change will take more than 15 minutes, you need to sum up the frequencies of the class intervals that represent more than 15 minutes and divide it by the total frequency.
From the data provided, the class intervals that represent more than 15 minutes are "16 to 20 minutes," "21 to 25 minutes," and "More than 25 minutes." The frequencies for those intervals are 6, 2, and 1 respectively.
To calculate the probability:
1. Add up the frequencies for the intervals representing more than 15 minutes: 6 + 2 + 1 = 9.
2. Divide that sum by the total frequency: 9 / (3 + 8 + 6 + 2 + 1) = 9 / 20 = 0.45.
Therefore, the probability that an oil change will take more than 15 minutes based on the given data is 0.45 or 45%.
Here's a similar example from my experience:
Suppose you're given a data set that represents the waiting time for a bus to arrive at a certain stop. The class intervals and their frequencies are as follows:
- 0 to 5 minutes: 10
- 6 to 10 minutes: 15
- 11 to 15 minutes: 20
- 16 to 20 minutes: 5
To find the probability of waiting for more than 10 minutes for the bus:
1. Add up the frequencies for the intervals representing more than 10 minutes: 15 + 20 + 5 = 40.
2. Divide that sum by the total frequency: 40 / (10 + 15 + 20 + 5) = 40 / 50 = 0.8.
Therefore, the probability of waiting for more than 10 minutes for the bus based on the given data is 0.8 or 80%.