Question

the results of a certain medical test are normally distributed with a mean of 124 and a standard deviation of 13. 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 112 and 136. click the icon to view the table of z - scores and percentiles. the percentage of people with readings between 112 and 136 is %. (round to two decimal places as needed.)

Explanation:

Step1: Calculate z - score for 112

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu = 124$, $\sigma=13$ and $x = 112$.
$z_1=\frac{112 - 124}{13}=\frac{- 12}{13}\approx - 0.92$

Step2: Calculate z - score for 136

Using the same formula with $x = 136$, $\mu = 124$ and $\sigma = 13$.
$z_2=\frac{136-124}{13}=\frac{12}{13}\approx0.92$

Step3: Find the percentiles

From the z - score table, the percentile corresponding to $z=-0.92$ is approximately $0.1788$ and the percentile corresponding to $z = 0.92$ is approximately $0.8212$.

Step4: Calculate the percentage between the two values

The percentage of people with readings between 112 and 136 is $P(112

Answer:

$64.24$