Given:
The weight of 18-month-old girls is normally distributed with a mean of 24.8 pounds and a standard deviation of 2.9 pounds. The table of z-score percentile is given.
Required:
Find the percentile of the 18-month-old girl whose weight is between 19.1 and 23.6 pounds.
Explanation:
First, find the z-score by using the formula:
[tex]z-score=\frac{data\text{ item-mean}}{standard\text{ deviation}}[/tex][tex]\begin{gathered} z_{19.1}=\frac{19.1-24.8}{2.9} \\ z_{19.1}=\frac{-5.7}{2.9} \\ z_{19.1}=-1.9655 \\ z_{19.1}\approx-2.0 \end{gathered}[/tex][tex]\begin{gathered} z_{23.6}=\frac{23.6-24.8}{2.9} \\ z_{23.6}=\frac{-1.2}{2.9} \\ z_{23.6}=-0.4137 \\ z_{23.6}\approx-0.41 \end{gathered}[/tex]
Now by using the table find the percentile corresponding to the z-score.
The percentile corresponds to z-score -2.0 = 2.28
The percentile corresponds to z-score -0.41 = 34.46
Find the difference between the percentile =
[tex]\begin{gathered} 34.46-2.28=32.18 \\ \approx32.18 \end{gathered}[/tex]
Thus the 18-month-old girl's weight between 19.1 and 23.6 pounds is 32.18%.
Final Answer:
32.18%
