Hypertension people are classified as hypertensive if their...

Hypertension People are classified as hypertensive if their systolic blood pressure (SBP) is higher than a specified level for their age group, according to the algorithm in the following table. Assume SBP is normally distributed with mean and standard deviation given in the following table for age groups 1-14 and 15-44, respectively. Define a family as a group of two people in age group 1-14 and two people in age group 15-44. A family is classified as hypertensive if at least one adult and at least one child are hypertensive. (Round your answers to four decimal places.) Mean and standard deviation of SBP (mm Hg) in specific age groups Age group Mean Standard deviation Specified hypertension level 1-14 105.0 5.0 115.0 15-44 125.0 10.0 140.0 USE SALT (a) What proportion of 1- to 14-year-olds are hypertensive? 0.0228 (b) What proportion of 15- to 44-year-olds are hypertensive? 0.0668 (c) What proportion of families are hypertensive? (Assume that the hypertensive status of different members of a family are independent random variables.) 0.1684 x (d) Suppose a community has 1,100 families living in it. What is the probability that between one and seven families are hypertensive? 0.8120 x

Transcript

00:01 In this question, we are looking at a normal distribution, so i will start by drawing it.

00:06 The total area under this curve is 1, or 100%, and it's symmetric.

00:12 So half of women will have a blood pressure below the mean, half above the mean.

00:17 The mean, mu, is 114 .8, standard deviation sigma, 13 .1.

00:27 And for part a, we want to know the probability of a randomly selected woman having hypertension.

00:35 So 140, the cutoff point for hypertension, is above the mean.

00:41 Put it there.

00:42 We want the probability of falling into this area.

00:45 If i find this area, i have my answer.

00:49 So, my next step is to find the corresponding z score.

00:53 Z is x minus mu over sigma.

00:59 So, 140 minus 114 .8 divided by 13 .1, not a nice number, i'll leave it in a exact form.

01:10 25 .2 over 13 .1.

01:13 But it's about 1 .92.

01:15 And yep, it hasn't told us to round our z scores, so i will use exact values.

01:22 So 140 is this many standard deviations above the mean.

01:25 Now i need to turn it into an area under the curve.

01:28 I have two tools at my disposal.

01:30 The standard and the cumulative normal functions.

01:33 Standard is area between x and mu.

01:39 So i put in my z score, i get this bit.

01:41 Not what i want, but if i take it away from 0 .5, i have my answer.

01:46 Cumulative is area to the left.

01:50 Everything i don't want.

01:52 Take it away from 1.

01:53 I have my answer.

01:56 I'm going to use the standard function, but you can use either 1.

02:00 You can find these functions on your graphical calculator, or software like excel, or r.

02:05 There are also z score tables, but i don't like to use those unless i'm told to use them, because they make you round your z score.

02:11 And here i can use the exact value if i use my calculator.

02:15 So i put that into the standard function, get 0 .4 -7 -8, which leaves my answer, 0 .0 .272.

02:24 So there's part a.

02:27 For part b, now we are not looking at individuals, but at a group of four women.

02:33 So we're taking a random sample of size 4.

02:36 We want to know the probability the average is greater than 140.

02:41 Well, i know the shape of the distribution for individuals, so sample size 1.

02:47 Do i know anything about the shape of the distribution for means of four women? yes, i know that if you take every possible sample of four women, find the average blood pressure and plot these means out, you will get another normal distribution.

03:05 Because the original distribution is normal, any sampling distribution based on it will also be normal...

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