The following are the duration in minutes of a sample of...

The following are the duration in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier. Relative Time (in Minutes) Frequency 0 but less than 5 0.37 5 but less than 10 0.22 10 but less than 15 0.15 15 but less than 20 0.10 20 but less than 25 0.07 25 but less than 30 0.07 30 or more 0.02 a. What is the width of each class? b. If 1,000 calls were randomly sampled, how many calls lasted under 10 minutes? c. If 100 calls were randomly sampled, how many calls lasted 15 minutes or longer? d. If 10 calls lasted 30 minutes or more, how many calls lasted less than 5 minutes? What is the cumulative relative frequency for the percentage of calls that lasted under 20 minutes? What is the cumulative relative frequency for the percentage of calls that lasted 10 minutes or more? If 100 calls were randomly sampled, ________ of them would have lasted at least 15 minutes but less than 20 minutes. If 100 calls were sampled, ________ of them would have lasted less than 15 minutes. If 100 calls were sampled, ________ of them would have lasted 20 minutes or more. If 100 calls were sampled, ________ of them would have lasted less than 5 minutes or at least 30 minutes or more.

Transcript

00:01 So a long -distance carrier recorded the percentages of phone calls that lasted between certain time periods.

00:10 So this chart is saying that 37 % of the calls lasted between 0 and 5 minutes, 22 % of the calls lasted between 5 and 10, and so forth.

00:22 So in part a, we want to calculate or discuss the class with, and to calculate class.

00:32 Class width, it is the difference between the beginning of two consecutive classes.

00:39 So the difference between these two consecutive classes is five, the difference between these two consecutive classes is five, the difference between these two is five, so therefore our class with is five.

00:56 In part b, if a thousand calls are randomly sampled, how many calls? lasted under 10 minutes.

01:07 So under 10 minutes would be these calls here.

01:15 So under 10 minutes accounts for .59 or 59 percent.

01:26 So we could set up a proportion.

01:29 59 percent means 59 out of every hundred is comparable to how many out of a thousand.

01:39 So i could cross -multiply here and i would get 100x is equal to 59 ,000.

01:48 So the x would have to be 590 calls.

01:56 So in summary there, if a thousand calls were randomly sampled, then we would expect 590 calls to last under 10 minutes.

02:08 In part c, we are focusing on the calls that lasted 15 minutes or longer.

02:19 So that would be here.

02:24 So 15 minutes or longer.

02:32 And when i add those up, they add up to .26.

02:37 So what that is saying is 26 out of 100 is equal to what out of 100 calls.

02:50 So if i were to cross multiply that or if i just think in terms of equivalent fractions, then x must be 26 calls.

02:59 So if i were to select 100 calls randomly sampled, then i should expect 26 calls lasted 15 minutes or longer.

03:10 In part d, part d is slightly different.

03:15 So in part d, we are going to now add on a new column.

03:28 And we're going to call that column frequency.

03:37 And in part d, it says if 10 calls lasted 30 minutes.

03:41 So we know that 10 calls lasted 30 minutes or more.

03:49 What we want to determine is how many calls lasted less than five.

03:58 So we've got to ultimately figure out right here.

04:02 So in order to do so, we're going to first figure out how many total calls were there.

04:08 So we know that 10 of the unknown number of calls is equal to 2 % or 2 out of 100, where again, x is representing total number of calls.

04:29 So if we were to cross multiply here, we'd get 2x equals 1 ,000.

04:34 So that means we have 500 total calls.

04:43 So i could say the sum of the frequencies is 500.

04:48 So now i can calculate that i know that 37 % of that 500, 37 % of that 500 is going to be in the under five minute category...

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