Let's examine each data set to determine if it is likely to be normally distributed:
1. The weights of the babies born at a hospital:
- Baby weights follow a distribution where most of the data points are around a central value (mean) with fewer data points as you move away from the mean. Thus, it is reasonable to conclude that the weights of babies are likely to be normally distributed.
- Answer: Yes
2. The number of babies born each month at a hospital:
- The number of babies born each month is a count variable that typically follows a Poisson distribution or could be influenced by seasonal trends and other factors. Hence, it is not necessarily normally distributed.
- Answer: No
3. The number of rooms on each floor of a hospital:
- The number of rooms is a fixed count that can vary significantly between floors but does not generally follow a normal distribution curve. It tends to be more discrete and less likely to be spread out in the way a normal distribution would imply.
- Answer: No
4. The lengths of the babies born at a hospital:
- Similar to weights, the lengths of babies can be expected to cluster around a central value with fewer occurrences of extremely short or extremely long babies, fitting the characteristics of a normal distribution.
- Answer: Yes
Putting these answers together, the correctly filled table should look like this:
\begin{tabular}{|l|c|}
\hline Data Set & Yes \\
\hline the weights of the babies born at a hospital & Yes \\
\hline the number of babies born each month at a hospital & No \\
\hline the number of rooms on each floor of a hospital & No \\
\hline the lengths of the babies born at a hospital & Yes \\
\hline
\end{tabular}
