To determine where a majority of the data lies in a dataset with a given mean and standard deviation, we can use the properties of the normal distribution.
The _mean_ of the dataset is given as 400 and the _standard deviation_ is 17. In a normal distribution:
- Approximately 68% of the data lies within one standard deviation of the mean.
This means we need to find the range that is one standard deviation below and one standard deviation above the mean.
1. Calculate the lower bound:
- Subtract the standard deviation from the mean.
- [tex]\( \text{Mean} - \text{Standard Deviation} \)[/tex]
- [tex]\( 400 - 17 = 383 \)[/tex]
2. Calculate the upper bound:
- Add the standard deviation to the mean.
- [tex]\( \text{Mean} + \text{Standard Deviation} \)[/tex]
- [tex]\( 400 + 17 = 417 \)[/tex]
Therefore, the majority of the data will lie between 383 and 417.
The correct answer is:
B. 383 to 417.
