Question

1. systolic blood pressure readings for a population of adults are normally distributed, with a mean of 122 mmhg and a standard deviation of 14 mmhg. the systolic blood pressure for an adult who cuts off the lowest quarter of this distribution would be

a. between 94 and 108 mmhg.
b. between 108 and 122 mmhg.
c. between 122 and 136 mmhg.
d. between 136 and 150 mmhg.
e. above 150 mmhg.

Explanation:

Step1: Find the z - score for the lower quartile

The lower quartile (25th percentile) has a z - score (from the standard normal distribution table) of approximately $z=- 0.67$.

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value we want to find, $\mu$ is the mean, and $\sigma$ is the standard deviation. We know $\mu = 122$, $\sigma=14$, and $z=-0.67$. Rearranging the formula for $x$ gives $x=\mu + z\sigma$.

Step3: Calculate the value of $x$

Substitute the values into the formula: $x = 122+(-0.67)\times14=122 - 9.38 = 112.62$.

Answer:

B. between 108 and 122 mmHg.