Question

the weights for 12 - month - old males are normally distributed with a mean of 22.4 pounds and a standard deviation of 2.2 pounds. use the given table to find the percentage of 12 - month - old males who weigh between 16.9 and 18 pounds. click the icon to view the table of z - scores and percentiles. % of 12 - month - old males weigh between 16.9 and 18 pounds. (round to two decimal places as needed.)

Explanation:

Step1: Calculate z - score for \(x = 16.9\)

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 22.4\) (mean) and \(\sigma=2.2\) (standard deviation). For \(x = 16.9\), \(z_1=\frac{16.9 - 22.4}{2.2}=\frac{- 5.5}{2.2}=-2.5\)

Step2: Calculate z - score for \(x = 18\)

Using the same formula, for \(x = 18\), \(z_2=\frac{18 - 22.4}{2.2}=\frac{-4.4}{2.2}=-2\)

Step3: Use the z - score table

The z - score table gives the area to the left of the z - score. The area to the left of \(z_1=-2.5\) is \(0.0062\) and the area to the left of \(z_2 = - 2\) is \(0.0228\)

Step4: Find the percentage between the two z - scores

The percentage of data between \(z_1\) and \(z_2\) is \(P(-2.5<Z<-2)=0.0228 - 0.0062=0.0166\)

Answer:

\(1.66\%\)