The following are the duration in minutes of a sample of long-distance phone calls.
Relative
Time (in Minutes) Frequency
0 but less than 2 0.30
2 but less than 4 0.20
4 but less than 6 0.25
6 but less than 8 0.10
8 but less than 10 0.07
10 but less than 12 0.05
12 or more 0.03
If 20 calls lasted 10 minutes or more, how many calls lasted less than 4 minutes?
110
195
125
200
To find the total number of calls that lasted less than 4 minutes, we need to add up the frequencies for the first three intervals: 0.30 + 0.20 + 0.25 = 0.75.
Since we know that the sum of all the frequencies must equal 1, we can subtract 0.75 from 1 to find the total frequency of calls that lasted 4 minutes or longer: 1 - 0.75 = 0.25.
Since there were 20 calls that lasted 10 minutes or more, we can find the total number of calls by dividing the frequency for 10 minutes or more by the frequency of 10 minutes or more: 20 / 0.05 = 400.
Now that we know there were 400 total calls, we can find how many calls lasted less than 4 minutes: 0.75 * 400 = 300.
So, out of the 400 total calls, 300 calls lasted less than 4 minutes.