SOLUTION: 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

Question 658836: 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 by Theo(13342) (Show Source): You can put this solution on YOUR website!
a calculator that can be used to find your answer easily is at the following link:
http://davidmlane.com/normal.html
you would put inputs into this calculator as shown in the following picture.
picture not found

in the above table, you enter the mean of 120 and the standard deviation of 12 and then you click on between and enter 96 for the low score and 144 for the high score.
you can also get your output by translating the raw scores into z scores and enter the following inputs into the calculator as shown in the following picture.
picture not found

in the second version, you are entering a mean of 0 and a standard deviation of 1 and you are clicking on between and entering -2 for the low score and +2 for the high score.

to determine how to calculate the z-score, do the following.
mean = 120
standard deviation = 12
you want to find the area under the distribution curve between the scores of 96 and 144.
to find the z-score for the low score, your formula will be:
low z-score = (96 - 120) / 12 = -24/12 = -2.
to find the z-score for the high score, your formula will be:
high z-score = (144 - 120) / 12 = +24/12 = +2.
the + sign is normally silent (not shown) but i show it here to emphasize that you are going from a low z-score of -2 to a high z-score of +2.

when you use z-scores, the mean is always 0 and the standard deviation is always 1.

in both case, you see that the area under the distribution curve is equal to .9545 which is equivalent to 95.45%.

the general formula to find the z-score is (raw score - mean) / standard deviation

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