Question

the results of a certain medical test are normally distributed with a mean of 129 and a standard deviation of 11. convert the given results into z - scores, and then use the accompanying table of z - scores and percentiles to find the percentage of people with readings between 123 and 135. click the icon to view the table of z - scores and percentiles. the percentage of people with readings between 123 and 135 is % (round to two decimal places as needed.)

Explanation:

Step1: Calculate z - score for 123

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu = 129$, $\sigma=11$ and $x = 123$.
$z_1=\frac{123 - 129}{11}=\frac{-6}{11}\approx - 0.55$

Step2: Calculate z - score for 135

Using the same formula with $x = 135$, $\mu = 129$ and $\sigma = 11$.
$z_2=\frac{135 - 129}{11}=\frac{6}{11}\approx0.55$

Step3: Find percentiles from z - score table

From the z - score table, the percentile corresponding to $z_1=-0.55$ is $0.2912$, and the percentile corresponding to $z_2 = 0.55$ is $0.7088$.

Step4: Calculate the percentage between the two values

The percentage of people with readings between 123 and 135 is $0.7088-0.2912 = 0.4176$.

Answer:

$41.76$