Question

Check our blood pressure: In a recent study, the Centers for Disease Control and prevention reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean 80.7 and a standard deviation of 10.1. (a) What proportion of women have blood pressures lower than 68?

Answer 1

Answer:

The proportion of the women that have blood pressures lower than 68 is 0.1038 or 10.38%.

Step-by-step explanation:

Given:

Blood pressure required (x) = 68

Mean blood pressure (μ) = 80.7

Standard deviation (σ) = 10.1

The distribution is normally distributed.

So, first, we will find the z-score of the distribution using the formula:

$z=\frac{x-\mu}{\sigma}$

Plug in the values and solve for 'z'. This gives,

$z=\frac{68-80.7}{10.1}=-1.26$

So, the z-score of the distribution is -1.26.

Now, we need the probability $P(x\leq 68 )=P(z\leq -1.26)$.

From the normal distribution table for z-score equal to -1.26, the value of the probability is 0.1038. This is the area to the left of the curve or less than z-score value which is what we need.

Therefore, the proportion of the women that have blood pressures lower than 68 is 0.1038 or 10.38%.