Question

Use the empirical rule to solve the problem. 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. what percentage of 18-year-old women have a systolic blood pressure between 96 mmhg and 144 mmhg

Answer 1

First you need to determine how much standard deviation the range is. 
120+12*x= 96
x= 96-120/ 12= -2

120+12*y=144
y= 144-120/12= +2

Systolic blood pressure between 96 mmHg and 144 mmHg means that the blood pressure is at -2SD to +2SD. The Z-score for -2SD is 0.0228 and +2SD is 0.9772
So the percentage would be: 0.9772- 0.0228  * 100%= 95.44%

Answer 2

Answer:

is the 30 % of the population

Explanation:

If the Standard deviation is 12 mmHg, that mean that 1 SD up and down from the average value will be:

Up: 120 + 12 = 132 mmHg

Down: 120 - 12 = 108 mmHg

If we continue calculating the second standard deviation, will be:

Up: 132 + 12 = 144 mmHg

Down: 108 - 12 = 96 mmHg

This calculation represent that the values are 2 SD apart from the avegare, and if we check the graphic, in a normal distribution, will mean that the percentage of the women in this pressure blood situation will be 30 %, 15 % to the smaller value and 15 % to the bigger value.

Hope this info is useful.