Question

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

Answer:

95.4% of 18-year-old women have a systolic blood pressure between 96 mm Hg and 144 mm Hg.      

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 120 mm Hg

Standard Deviation, σ = 12 mm Hg

We are given that the distribution of systolic blood pressure is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(blood pressure between 96 mm Hg and 144 mm Hg)

$P(96 \leq x \leq 144) = P(\displaystyle\frac{96 - 120}{12} \leq z \leq \displaystyle\frac{144-120}{12}) = P(-2 \leq z \leq 2)\\\\= P(z \leq 2) - P(z < -2)\\= 0.977 - 0.023 = 0.954 = 95.4\%$

$P(96 \leq x \leq 144) = 95.4\%$

95.4% of 18-year-old women have a systolic blood pressure between 96 mm Hg and 144 mm Hg.