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\begin{tabular}{|c|c|c|}
\hline Age & Mean & \begin{tabular}{c}
Standard \\
Deviation
\end{tabular} \\
\hline 7 years & 49 inches & 2 inches \\
\hline
\end{tabular}

According to the empirical rule, [tex]68\%[/tex] of 7-year-old children are between [tex]47[/tex] inches and [tex]51[/tex] inches tall.

[tex]95\%[/tex] of 7-year-old children are between [tex]\square[/tex] inches and [tex]\square[/tex] inches tall.



Answer :

GinnyAnswer
Sure! Let's solve the problem:

We are given that:

- The mean height for 7-year-old children is 49 inches.
- The standard deviation of the height is 2 inches.

According to the empirical rule (also known as the 68-95-99.7 rule):

- 68% of data lies within 1 standard deviation of the mean.
- 95% of data lies within 2 standard deviations of the mean.
- 99.7% of data lies within 3 standard deviations of the mean.

To determine the range in which 95% of the 7-year-old children fall, we need to calculate the range within 2 standard deviations of the mean.

Step 1: Calculate the lower bound of the height range.
[tex]\[ \text{Lower bound} = \text{mean} - 2 \times \text{standard deviation} \][/tex]
[tex]\[ \text{Lower bound} = 49 - 2 \times 2 \][/tex]
[tex]\[ \text{Lower bound} = 49 - 4 \][/tex]
[tex]\[ \text{Lower bound} = 45 \][/tex]

Step 2: Calculate the upper bound of the height range.
[tex]\[ \text{Upper bound} = \text{mean} + 2 \times \text{standard deviation} \][/tex]
[tex]\[ \text{Upper bound} = 49 + 2 \times 2 \][/tex]
[tex]\[ \text{Upper bound} = 49 + 4 \][/tex]
[tex]\[ \text{Upper bound} = 53 \][/tex]

Therefore, 95% of 7-year-old children are between 45 inches and 53 inches tall.

To complete the table:

[tex]\[ 95\% \text{ of 7-year-old children are between } 45 \text{ inches and } 53 \text{ inches tall.} \][/tex]

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