1) high blood pressure, such as systolic pressure over 140 mmhg, is a risk factor for heart disease. medical…

1) high blood pressure, such as systolic pressure over 140 mmhg, is a risk factor for heart disease. medical data indicates that the systolic blood pressure of all males aged 20 and over follows a normal distribution with mean 125 mmhg and standard deviation 15 mmhg. use the empirical rule and find the percentage of males ages 20 and over who have systolic blood pressure over 140 mmhg. a) draw and shade the normal distribution curve b) interpret the results in a complete sentence

1) high blood pressure, such as systolic pressure over 140 mmhg, is a risk factor for heart disease. medical data indicates that the systolic blood pressure of all males aged 20 and over follows a normal distribution with mean 125 mmhg and standard deviation 15 mmhg. use the empirical rule and find the percentage of males ages 20 and over who have systolic blood pressure over 140 mmhg. a) draw and shade the normal distribution curve b) interpret the results in a complete sentence

Answer

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 140$, $\mu=125$, and $\sigma = 15$. So $z=\frac{140 - 125}{15}=\frac{15}{15}=1$.

Step2: Apply the empirical rule

The empirical rule for a normal distribution states that about 68% of the data lies within 1 standard - deviation of the mean ($\mu\pm\sigma$), about 95% lies within 2 standard - deviations of the mean ($\mu\pm2\sigma$), and about 99.7% lies within 3 standard - deviations of the mean ($\mu\pm3\sigma$). The area within 1 standard - deviation of the mean is 68%, so the area outside of $\mu\pm1\sigma$ is $100 - 68=32%$. Since the normal distribution is symmetric, the area above $z = 1$ is $\frac{100 - 68}{2}=16%$.

a)

To draw the normal distribution curve:

  1. Draw a bell - shaped curve. Mark the mean $\mu = 125$ in the center of the x - axis.
  2. Mark the values $\mu-\sigma=125 - 15 = 110$, $\mu+\sigma=125+15 = 140$, $\mu - 2\sigma=125-30 = 95$, $\mu + 2\sigma=125 + 30=155$, $\mu-3\sigma=125 - 45 = 80$, $\mu + 3\sigma=125+45 = 170$ on the x - axis.
  3. Shade the area to the right of $x = 140$ (corresponding to $z = 1$).

b)

Approximately 16% of males aged 20 and over have a systolic blood pressure over 140 mmHg.

Answer:

a) Draw a bell - shaped curve with mean 125, mark 110, 140, 95, 155, 80, 170 on x - axis and shade area to right of 140. b) Approximately 16% of males aged 20 and over have a systolic blood pressure over 140 mmHg.