To determine where the majority of the data will lie, we first need to understand the properties of a normal distribution and how the mean and standard deviation define the spread of the data.
1. Mean: The mean is the average value of the dataset. For this dataset, the mean is 85.
2. Standard Deviation: This measures the amount of variation or dispersion in the dataset. A smaller standard deviation means the data points are close to the mean, while a larger standard deviation indicates that the data points are spread out. Here, the standard deviation is 12.
In a normal distribution:
- About 68% of the data lies within one standard deviation of the mean.
To find this range:
1. Calculate one standard deviation below the mean:
- Mean - Standard Deviation = 85 - 12 = 73
2. Calculate one standard deviation above the mean:
- Mean + Standard Deviation = 85 + 12 = 97
Therefore, the majority of the data will lie between 73 and 97.
Considering the options provided:
1. 73 to 97
2. 85 to 100
3. 55 to 85
The correct option is:
73 to 97.
