WEBVTT 1 00:00:03.510 --> 00:00:05.190 Hello students. 2 00:00:05.190 --> 00:00:06.960 Now we are going to continue working 3 00:00:06.960 --> 00:00:10.440 on problem three and we are going to go to part B. 4 00:00:10.440 --> 00:00:12.150 So again, I will read the problem. 5 00:00:12.150 --> 00:00:15.900 Total classroom in children age 10 to 15 years 6 00:00:15.900 --> 00:00:18.960 of age is assumed to follow a normal distribution 7 00:00:18.960 --> 00:00:23.281 with Amina 191 and a standard deviation of 22.4. 8 00:00:23.281 --> 00:00:26.397 Part B is asking us what proportion 9 00:00:26.397 --> 00:00:29.995 of children 10 to 15 years of age would be classified 10 00:00:29.995 --> 00:00:31.813 as hyperlipidemia. 11 00:00:31.813 --> 00:00:35.010 Assume that hyperlipidemia is defined 12 00:00:35.010 --> 00:00:37.939 as total cholesterol level over 200. 13 00:00:37.939 --> 00:00:41.503 So again, we have the same format and the same values. 14 00:00:41.503 --> 00:00:44.998 So as a first step, I'm going to write down the information 15 00:00:44.998 --> 00:00:47.935 we have and draw the normal curve. 16 00:00:47.935 --> 00:00:52.935 So our mu is equal to 191, our sigma is equal to 22.4. 17 00:00:56.759 --> 00:01:00.033 Okay? And this is our normal curve. 18 00:01:03.708 --> 00:01:08.708 Here is 191, here is X. 19 00:01:12.540 --> 00:01:15.840 So the question is asking us what is the area 20 00:01:15.840 --> 00:01:18.780 under the curve past 200? 21 00:01:18.780 --> 00:01:22.410 So what I'm going to do is I'm going to use another color to 22 00:01:22.410 --> 00:01:23.670 highlight that area. 23 00:01:23.670 --> 00:01:25.840 So let me use 24 00:01:27.990 --> 00:01:29.655 this color. 25 00:01:29.655 --> 00:01:30.683 It's kind of like purple. 26 00:01:31.620 --> 00:01:36.620 So here it is, 200 and we are looking for this area, okay? 27 00:01:37.050 --> 00:01:39.033 The area past 200. 28 00:01:43.290 --> 00:01:45.700 So as before, we have to now 29 00:01:49.170 --> 00:01:50.040 transform this 30 00:01:50.040 --> 00:01:53.400 to a Z distribution because otherwise we will not 31 00:01:53.400 --> 00:01:55.950 be able to perform the calculation. 32 00:01:55.950 --> 00:02:00.263 So for a Z distribution, we will have a mean of zero. 33 00:02:05.910 --> 00:02:08.400 So to find the respective values right now we have to 34 00:02:08.400 --> 00:02:12.150 go back to our formula, which is Z, equal 35 00:02:12.150 --> 00:02:16.383 to X minus mu divided by sigma. 36 00:02:19.200 --> 00:02:22.680 And here what we are trying to do is find the probability 37 00:02:22.680 --> 00:02:25.297 that X is greater than 200. 38 00:02:26.640 --> 00:02:31.640 So as we perform the transformation, we will be 39 00:02:31.680 --> 00:02:36.680 using the formula again, and that is 200 minus 191 divided 40 00:02:39.480 --> 00:02:40.850 by 22.4. 41 00:02:41.736 --> 00:02:45.383 Okay, oops, went 2, 2, 4. 42 00:02:48.030 --> 00:02:49.593 So again, this is the formula. 43 00:02:51.000 --> 00:02:53.190 So after we do the calculation here 44 00:02:53.190 --> 00:02:57.153 basically the algebra, we find out Z is greater than 0.40. 45 00:03:03.450 --> 00:03:04.530 So again, what do we do? 46 00:03:04.530 --> 00:03:06.420 We go to the back of our book. 47 00:03:06.420 --> 00:03:09.810 Now we will go to the positive side of the table. 48 00:03:09.810 --> 00:03:11.910 So first we look at the column 49 00:03:11.910 --> 00:03:16.207 and stop at the 0.4 value and look to the right. 50 00:03:16.207 --> 00:03:17.540 And there it is. 51 00:03:19.050 --> 00:03:23.910 And again, from the way our text is set up, the table here, 52 00:03:23.910 --> 00:03:27.060 the way the C table is set up for our text, 53 00:03:27.060 --> 00:03:29.550 what we have found is the probability 54 00:03:29.550 --> 00:03:33.600 of Z being less than 0.40. 55 00:03:33.600 --> 00:03:36.240 So here what we have is 56 00:03:36.240 --> 00:03:40.980 and again there is a little space issue here. 57 00:03:40.980 --> 00:03:44.887 So we have found Z is less than 0.40 58 00:03:49.200 --> 00:03:53.070 and that is equal to 0.6554. 59 00:03:56.490 --> 00:03:59.790 So basically now to highlight this in our table 60 00:03:59.790 --> 00:04:01.410 and I'm going to use a different color 61 00:04:01.410 --> 00:04:02.703 I'm going to use blue. 62 00:04:03.960 --> 00:04:07.830 So this is the value our table has given us. 63 00:04:07.830 --> 00:04:10.283 Okay? This part, okay, 64 00:04:13.595 --> 00:04:18.595 this part and let me go and color it much nicely. 65 00:04:22.110 --> 00:04:26.460 This is the part our table has given us, but we are looking 66 00:04:26.460 --> 00:04:29.673 for the part that is highlighted in purple. 67 00:04:32.161 --> 00:04:34.320 So how are we going to find it? 68 00:04:34.320 --> 00:04:38.190 So as I mentioned previously, we can do this very easily. 69 00:04:38.190 --> 00:04:41.520 Why? Because we know that the area under the curve, 70 00:04:41.520 --> 00:04:44.400 the entire area under the curve is one. 71 00:04:44.400 --> 00:04:48.633 So all we have to do right now is a little subtraction. 72 00:04:51.081 --> 00:04:56.081 So to find out P, the probability that C 73 00:04:57.150 --> 00:05:02.150 is greater than 0.40, we have to deduct 74 00:05:05.482 --> 00:05:10.482 from one that the probability Z is less than 0.40. 75 00:05:13.470 --> 00:05:16.320 Okay? So when we do that, what do we get? 76 00:05:16.320 --> 00:05:21.213 One minus 0.6554. 77 00:05:23.520 --> 00:05:28.520 And that answer will be 0.3446, or 34.46%. 78 00:05:37.620 --> 00:05:38.910 That is our answer. 79 00:05:38.910 --> 00:05:41.520 Okay, so what does this mean? 80 00:05:41.520 --> 00:05:42.933 This means that the given, 81 00:05:44.367 --> 00:05:48.330 if someone asks us what is the probability 82 00:05:48.330 --> 00:05:53.113 that the child is hyperlipidemia, we would say it is 34.46%. 83 00:05:54.480 --> 00:05:57.000 And again, please keep in mind that it's based 84 00:05:57.000 --> 00:05:59.763 on the values that are provided in this problem.