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Norma-Jean [14]
3 years ago
13

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?
Mathematics
1 answer:
Mariana [72]3 years ago
8 0

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.

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