Question

the weights for 12 - month - old males are normally distributed with a mean of 22.7 pounds and a standard deviation of 2.8 pounds. use the given table to find the percentage of 12 - month - old males who weigh between 17.1 and 18.5 pounds. click the icon to view the table of z - scores and percentiles. % of 12 - month - old males weigh between 17.1 and 18.5 pounds. (round to two decimal places as needed.)

Explanation:

Step1: Calculate z - score for 17.1 pounds

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean and $\sigma$ is the standard deviation. Given $\mu = 22.7$, $\sigma=2.8$ and $x = 17.1$. Then $z_1=\frac{17.1 - 22.7}{2.8}=\frac{- 5.6}{2.8}=-2$.

Step2: Calculate z - score for 18.5 pounds

Using the same formula with $x = 18.5$, we have $z_2=\frac{18.5 - 22.7}{2.8}=\frac{-4.2}{2.8}=-1.5$.

Step3: Find the percentiles from the z - score table

From the z - score table, the percentile corresponding to $z=-2$ is $0.0228$ and the percentile corresponding to $z = - 1.5$ is $0.0668$.

Step4: Calculate the percentage between the two values

The percentage of values between $z=-2$ and $z=-1.5$ is $P(-2

Answer:

$4.40\%$