We know that
• The mean is 9.75 meters per second.
,
• The standard deviation is 0.08 meters per second.
According to the empirical rule, 95% of the data falls into 2 standard deviations below and above the mean, so we just have to subtract and add the standard deviation twice.
[tex]\begin{gathered} \bar{x}+2\sigma \\ \bar{x}-2\sigma \end{gathered}[/tex]
Using the given information, we have
[tex]\begin{gathered} 9.75+2(0.08)=9.75+0.16=9.91 \\ 9.75-2(0.08)=9.75-0.16=9.59 \end{gathered}[/tex]
Therefore, her next measurement will fall between the values of 9.59 and 9.91 meters per second.
[tex]9.59
