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The following data represent the monthly phone use,in minutes, of a customer enrolled in a fraud preventionprogram for the past 20 months. The phone company decides...

Question

The following data represent the monthly phone use,in minutes, of a customer enrolled in a fraud preventionprogram for the past 20 months. The phone company decides to usethe upper fence as the cutoff point for the number of minutes atwhich the customer should be contacted. What is thecutoff point? 317384312394341354360403432503342338398311536470373328523381The cutoff point is ___ minutes.(Round to the nearest minute.)

The following data represent the monthly phone use, in minutes, of a customer enrolled in a fraud prevention program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. What is the cutoff point? 317 384 312 394 341 354 360 403 432 503 342 338 398 311 536 470 373 328 523 381 The cutoff point is ___ minutes. (Round to the nearest minute.)



Answers

As part of its "Customers First" program, a cellular phone company monitors monthly phone usage. The program identifies unusual use and alerts the customer that their phone may have been used by another person. The following data represent the monthly phone use in minutes of a customer enrolled in this program for the past 20 months. $$\begin{array}{lllll} 346 & 345 & 489 & 358 & 471 \\ \hline 442 & 466 & 505 & 466 & 372 \\ \hline 442 & 461 & 515 & 549 & 437 \\ \hline 480 & 490 & 429 & 470 & 516 \end{array}$$ The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. What is the cutoff point?

Okay with this problem. Um They're basically asking us to use a set of data to compare standard deviation and I. Q. R. When we change a data value and they go back and use the data from question number 25. Um where we were using cell phone usage and fraud. And so um the first thing they ask us to do is they ask us to use that data and go back and calculate standard deviation and like you are for the original set of data and I used my T I. 84 to do that. So the standard deviation um was just about 58. And then the I. Q. R. For this original set of data was 4 89.5. That's Q three minus Q. One which is 4 33. So that gives us an I. Q. R. Of 56.5. And that was minutes we were seeing how many minutes they spoke a month. Okay. And then on the second part um we were asked again to calculate standard deviation in I. Q. R. But it asked us to take the month that they spoke 346 minutes and change it to zero and think about how it's gonna affect standard deviation in I. Q. R. Now, think about what we're doing, we're taking 300 almost 50 minutes and we're turning it into zero. And so when we recalculate our stats, look at what happens. Standard deviation when that number become zero is right about 115 like it doubles compared to the 58. And then the I. Q. R. With our new data is 4 89.5 minus 4. 33 were using Q. Three and Q one to calculate I Q. R. 56.5. So our I. Q. R. Stays exactly the same. And what they're really wanting you to think about is we've talked about the term resistant Yeah. Whether a measure is resistant to extreme values or not, and what you want to realize is standard deviation is not resistant because that change had a great impact on the standard deviation. But like you are is resistant. So even though I changed that 3 52 0, the I Q R. Didn't change at all. Yeah. Yeah.

Hey, guys, welcome back of this problem when you want to start by reading the piece wise function. So we have that they cost per minute. Now, if you speak less than or equal to one minute of time. So if your minutes are less than or equal to one, the cost is free. I $0. Now, if your minutes are greater than one, the actual under the ceiling of em. This means that if you speak for one minute and 30 seconds, you know, get around death. Two minutes. If you speak for two minutes and 10 seconds, rather up to three minutes now. I went ahead and I graph this and does most for just for a few minutes. Here are some of our values. See and see that if you speak for just over a minute, it will go up to $2 appear. Do you speak for a little over two minutes? You up to $3 and so on and so forth. So now we want to figure out Will she exceed the 30 minutes of free calling with her calls? So the first call is two minutes and three seconds. Two minutes three seconds that will get rounded up with their ceiling function to three minutes. That she speaks for 13 minutes 46 seconds. 13 minutes 46 that gets rounded up to 14. Then she speaks for one minute, five seconds, one minute, five seconds. That gets rounded up to two minutes. Then she speaks for three minutes 59 seconds. That gets round it up to four minutes and she speaks for eight minutes, two seconds and that gets rounded up nine minutes. Now we can add all the values in this column. We have three plus 14 plus tube was four plus nine that is equal to 32 minutes. So based on this roundup system, she will indeed go over her 30 minute limit. She speaks for a total of 32 minutes with ceiling function. Now, if we just like her original talking time out of these values, we will find that she Onley actually uses the phone for 28 minutes and 55 seconds. That would be her actual usage so we can see that even though her actual usage was below the 30 minutes based on how this function worked on our Peace Prize function over here with the ceiling function, she still went over her 30 minute calling plan. Thanks for watching

So in part A If we're looking at minutes within that allotted amount, we're looking at the value of $30 distributed by all of the minutes. So our average is just 30 over tax, as that cost per minute for the first 250 minutes is somewhere where X balls greater than or equal to zero, but less than or equal to 250. If the user goes over this amount, then they're gonna follow a different equation, which happens to be that $30 fee distributed over the X minutes plus 300.6 per minutes. So this is for when X is greater than 250. This will be the cost. So in part C, if we're looking at 600 minutes, we want to use the expression from part B. So we have 30 over 600 plus 0.6. Um, this simplifies Teoh 0.5 plus 0.6 or, in other words, 65 cents 65th, hundreds of a dollar

Let's look at this cost problem. So the basic monthly plan is 5 $50 for 800 minutes. And the cell phone company charge additional, they will point to $2 per minute for every minute over 800. Okay so this customer spill, you know, let's look at the lowest feel first, the lowest um pio is Mhm. 67.16 Okay. We can't see that. Um 67.16 is over $50. Okay? So we used 67.16 minus five minus 50. Okay so this is a extra money. She pays for the cell phone company and we use it to divide 0.22 Okay so we can find the minutes over 800. Okay Which equals to 78 minutes. And now let's look at the highest, the highest bill is okay? Here I write, highest is $96.86. So we can find that. How many minutes does she uses? Over 800. Um So I can see 60 uh, 96.86 minus 50 over. There are 0.22 which is okay, which is 213 minutes. So the most minutes used in a single month is to 213 minutes. The least is 78 minutes.


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