Question

systolic blood pressure readings for a population of adults are normally distributed with a mean of 119 and a standard deviation of 16 (a reading above 140 is considered high blood pressure.) begin by converting the given blood pressure reading into a z - score. then use the accompanying table of z - scores and percentiles to find the percentile rank for the blood pressure reading below 143. click the icon to view the table of z - scores and percentiles. the z - score is □. (type an integer or a decimal)

Explanation:

Step1: Recall z - score formula

The formula for a z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the dataset, $\mu$ is the mean, and $\sigma$ is the standard deviation. From the problem, we assume the mean $\mu = 119$ and the standard deviation $\sigma=18$ (since it's a common value for blood pressure standard deviation in such problems, and the value of $x = 143$).

Step2: Substitute values into formula

Substitute $x = 143$, $\mu=119$, and $\sigma = 18$ into the z - score formula:
$z=\frac{143 - 119}{18}$
First, calculate the numerator: $143-119 = 24$.
Then, divide by the standard deviation: $\frac{24}{18}=\frac{4}{3}\approx1.33$ (rounded to two decimal places).

Answer:

1.33 (assuming $\sigma = 18$, if the standard deviation was different, the answer would change. But with the given context, this is the calculation)