Question

In 1998 the World Health Organization reported the findings of a major study on the quality of blood pressure monitoring around the world. In its report it stated that for Canada the results for diastolic blood pressure had a mean of 78 mmHg and a standard deviation of 11 mmHg. Assuming that diastolic blood pressure measurements are Normally distributed, the DBP reading that represents the 80th percentile of the distribution is _____.

Answer 1

Answer:

87.26 mm Hg is the reading that represents the 80th percentile of the distribution.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 78 mm Hg

Standard Deviation, σ = 11 mm Hg

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

Formula:

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

We have to find the value of x such that the probability is 0.80

P(X < x)  

$P( X < x) = P( z < \displaystyle\frac{x - 78}{11})=0.8$  

Calculation the value from standard normal z table, we have,  

$P(z < 0.842) = 0.8$

$\displaystyle\dfrac{x - 78}{11} = 0.842\\\\x = 87.262 \approx 87.26$

87.26 mm Hg is the reading that represents the 80th percentile of the distribution.