Question
A statistician collects the following height data in inches for a school district. The statistician says that it is a normal distribution. How did they draw this conclusion?
The frequencies for the first and last height range are the same.
The frequencies for each height range are different.
When graphed, the data creates a bell curve.
When graphed, the data creates a straight line.
The frequencies for the first and last height range are the same.
The frequencies for each height range are different.
When graphed, the data creates a bell curve.
When graphed, the data creates a straight line.
Answers
GPT-4o mini
To determine if the height data collected by the statistician is normally distributed, the most relevant conclusion would be:
**When graphed, the data creates a bell curve.**
A normal distribution is characterized by a specific bell-shaped curve when plotted, where most of the data points cluster around the mean, and the probabilities for values further away from the mean taper off symmetrically in both directions. The other options do not provide sufficient evidence of a normal distribution:
- The statement about the frequencies for the first and last height range being the same does not indicate normality.
- Different frequencies in each height range do not imply that the data is normally distributed.
- A straight line graph would suggest a linear relationship, not a normal distribution.
Thus, observing a bell curve in the graph supports the conclusion of normality in the data distribution.
**When graphed, the data creates a bell curve.**
A normal distribution is characterized by a specific bell-shaped curve when plotted, where most of the data points cluster around the mean, and the probabilities for values further away from the mean taper off symmetrically in both directions. The other options do not provide sufficient evidence of a normal distribution:
- The statement about the frequencies for the first and last height range being the same does not indicate normality.
- Different frequencies in each height range do not imply that the data is normally distributed.
- A straight line graph would suggest a linear relationship, not a normal distribution.
Thus, observing a bell curve in the graph supports the conclusion of normality in the data distribution.