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Select the correct answer.

A mother tracks the duration of her baby's three daily naps for a few weeks. The mean time, in minutes, and the standard deviation (SD) for each nap are recorded in the table below.

\begin{tabular}{|c|c|c|}
\hline
[tex]$1^{\text{st}}$[/tex] Nap & [tex]$2^{\text{nd}}$[/tex] Nap & [tex]$3^{\text{rd}}$[/tex] Nap \\
\hline
Mean [tex]$= 83$[/tex] & Mean [tex]$= 52$[/tex] & Mean [tex]$= 39$[/tex] \\
SD [tex]$= 9$[/tex] & SD [tex]$= 6$[/tex] & SD [tex]$= 11$[/tex] \\
\hline
\end{tabular}

Use the information in the table to select the true statement.

A. The [tex]$3^{\text{rd}}$[/tex] nap is the least consistent in duration because its standard deviation is the highest.
B. The [tex]$1^{\text{st}}$[/tex] nap is the least consistent in duration because its mean is the highest.
C. The [tex]$2^{\text{nd}}$[/tex] nap is the least consistent in duration because its standard deviation is the lowest.
D. The [tex]$3^{\text{rd}}$[/tex] nap is the least consistent in duration because its mean is the lowest.

Sagot :

GinnyAnswer
To determine the correct statement regarding the consistency of the baby's naps, we need to focus on the standard deviations provided in the data. The standard deviation is a measure of the amount of variation or dispersion in a set of values. A higher standard deviation indicates less consistency because the values are more spread out from the mean.

Here are the details given:
- [tex]\(1^{\text{st}}\)[/tex] Nap: Mean = 83 minutes, Standard Deviation (SD) = 9 minutes
- [tex]\(2^{\text{nd}}\)[/tex] Nap: Mean = 52 minutes, Standard Deviation (SD) = 6 minutes
- [tex]\(3^{\text{rd}}\)[/tex] Nap: Mean = 39 minutes, Standard Deviation (SD) = 11 minutes

We are interested in determining which nap is the least consistent in duration, which would correspond to the highest standard deviation. Let's compare the standard deviations for each nap:
- Standard Deviation of [tex]\(1^{\text{st}}\)[/tex] Nap: 9 minutes
- Standard Deviation of [tex]\(2^{\text{nd}}\)[/tex] Nap: 6 minutes
- Standard Deviation of [tex]\(3^{\text{rd}}\)[/tex] Nap: 11 minutes

We see that the [tex]\(3^{\text{rd}}\)[/tex] nap has the highest standard deviation (11 minutes), indicating that it has the greatest variability in duration and is therefore the least consistent.

Thus, the correct statement is:
A. The [tex]\(3^{\text{rd}}\)[/tex] nap is the least consistent in duration because its standard deviation is the highest.
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