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?

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:

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

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

Now, we need the probability .

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%.

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