) For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. a) If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is greater than 125.
The probability distribution of the standard normal variable, Z, is tabulated.
Z, the standard normal variable, is defined by:
- Z = (X - μ) / σ, where
- X is a normal variable (the systolic blood pressure,in mm Hg in this case)
- μ is the mean (114.8 mm Hg in this case), and
- σ is the standard deviation (13.1 mm Hg in this case).
You want to find the probablity that the systolic pressure of a woman between the ages of 18 and 24 is greater than 125, which means P (X > 125).
Then, to use a table of Z-score, you have to convert X > 125 into Z and find the corresponding probabiiity.
These are the calculations:
- X > 125 ⇒ Z > (125 - 114.8) / 13.1 ⇒ Z > 10.2 / 13.1 ⇒ Z > 0.7786
Now use a table for the normal standard probabiity. Most tables use two decimals for Z, so you can round to Z > 0.78, which will yield P (Z > 0.78) = 0.2177.
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Mathematics, published 11.05.2023
Mathematics, published 23.03.2023