Question

The mean of the systolic blood pressure of adults is μ=128.4
, and the standard deviation is σ=19.6
. What is the probability that an adult has a systolic blood pressure below 108.8?(1 point)
Responses

84%
84%

15.85%
15.85%

16%
16%

34%

Answer 1

To find the probability that an adult has a systolic blood pressure below 108.8, we will use the properties of the normal distribution.

1. First, we need to calculate the z-score for the systolic blood pressure of 108.8 using the following formula:

\[
z = \frac{(X - \mu)}{\sigma}
\]

Where:
- \(X\) is the value we are interested in (108.8),
- \(\mu\) is the mean (128.4),
- \(\sigma\) is the standard deviation (19.6).

Plugging in the values:

\[
z = \frac{(108.8 - 128.4)}{19.6} = \frac{-19.6}{19.6} = -1
\]

2. Now we will use the z-score to find the probability. We can look up the z-score of -1 in the standard normal distribution table, or use a calculator.

The probability corresponding to \(z = -1\) is approximately 0.1587 (or 15.87%).

Thus, the probability that an adult has a systolic blood pressure below 108.8 is approximately **15.85%**.

So the correct response is **15.85%**.