Question

Help please. I don't get this at all

The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. Using the empirical rule, what percentage of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg?

Answer 1

@amistre64

Answer 2

@pooja195

Answer 3

how is the empirical rule defined?>

Answer 4

The three stigma rule : 68-95-99.7

Answer 5

thats the one. now how can we apply it here?

Answer 6

remember, it gives us a basic rule of measurement for the number of standard deviations from the mean

Answer 7

I do not understand standard deviation either :/

Answer 8

so if we know how many times the standard deviation fits between a given x value, the the mean, we can assess the rule

Answer 9

standard deviation, its a 'unit' measure of spread.

for example, lets say every 3 feet is equal to 1 unit of measure

how many units of measure are in 13 feet? 13/3 of course

Answer 10

our stated unit measure given is 12 in this case.

how many 12s fit between 120 and 96?
how many 12s fit between 120 and 144?

Answer 11

Do I just divide?

Answer 12

well, essentially yes. but we have to first determine the distance between the mean and its endpoint, then divide.

(120-96)/12
and
(120-144)/12

Answer 13

Oh, so 2, -2

Answer 14

in general, a formula can be used to find the 'z score' (the number of standard deviation x is from the mean)

z = (x-mean)/sd

Answer 15

yep

so we are 2 sds to the left of the mean, and 2 sds to the right of the mean

so the empirical rule gives us what for a spread that is +-2 sds from the mean?

Answer 16

I am lost on what you mean now.

Answer 17

good thing i had you define the empirical rule :) now lets use it

The three stigma rule : 68-95-99.7

1 sd from the mean gives us about 34%,
so between -1 and 1 sds we have 34+34 = 68%

2 sd from the mean gives us about 47.5 %
so between -2 and 2 sds we have 47.5+47.5 = 95%

Answer 18

How do you find what you have from 2sd though? by that I mean how does -2 and 2 =47.5?

Answer 19

a picture usually accompanies the empirical rule, something like:

Answer 20

Is it 2.5 or 2.35? Idk if that makes a difference or not.

Answer 21

depends on the text :)

Answer 22

but if you can understand the picture, then you can determine how the empircal rule helps us estimate stuff

Answer 23

Oh, alright. So how does 2.5 and 2,-2 = 47.5 i'm still confused on that.

Answer 24

spose we had found that we were -2 to 1: then we would add up: 13.5 + 34 + 34