We know that
• The average is 7 pounds.
,
• The standard deviation is 1.23 pounds.
To label 3 standard deviations on the right, we have to add them to the mean. To label 3 standard deviations on the left, we have to subtract from the mean.
Right.
[tex]\begin{gathered} 7+1.23=8.23 \\ 8.23+1.23=9.46 \\ 9.46+1.23=10.69 \end{gathered}[/tex]
Left.
[tex]\begin{gathered} 7-1.23=5.77 \\ 5.77-1.23=4.54 \\ 4.54-1.23=3.31 \end{gathered}[/tex]
Let's sketch the graph
Let's find Jessica's and Maria's z-score.
[tex]\begin{gathered} Z_{\text{Jessica}}=\frac{x-\mu}{\sigma}=\frac{5.4-7}{1.23}=\frac{-1.6}{1.23}=-1.3_{} \\ Z_{\text{Maria}}=\frac{x-\mu}{\sigma}=\frac{9.8-7}{1.23}=\frac{2.8}{1.23}=2.3 \end{gathered}[/tex]
Maria's daughter's weight could be considered an outlier because it's far away from the mean of 7 pounds.
So, we should be concerned about Maria's daughter because her way is too high.
