Question
A sample data set with a mean on 685 and a standard deviation of 39.8 has a bell-shaped distribution. What range of values include approximately 68% of the data?
1)between 656.2 and 703.8
2)between 645.4 and 724.8
3)between 565.6 and 804.4
4)between 605.4 and 764.6
1)between 656.2 and 703.8
2)between 645.4 and 724.8
3)between 565.6 and 804.4
4)between 605.4 and 764.6
Answers
GPT-4o mini
In a bell-shaped distribution (normal distribution), approximately 68% of the data falls within one standard deviation of the mean.
Given:
- Mean (\(\mu\)) = 685
- Standard deviation (\(\sigma\)) = 39.8
To find the range that includes approximately 68% of the data, we calculate:
- Lower bound: \(\mu - \sigma = 685 - 39.8 = 645.2\)
- Upper bound: \(\mu + \sigma = 685 + 39.8 = 724.8\)
So, the range that includes approximately 68% of the data is between 645.2 and 724.8.
Looking at the provided options:
1) between 656.2 and 703.8
2) between 645.4 and 724.8
3) between 565.6 and 804.4
4) between 605.4 and 764.6
The correct answer is **2) between 645.4 and 724.8**. Note that 645.4 is very close to the calculated lower bound 645.2, making it a suitable approximation.
Given:
- Mean (\(\mu\)) = 685
- Standard deviation (\(\sigma\)) = 39.8
To find the range that includes approximately 68% of the data, we calculate:
- Lower bound: \(\mu - \sigma = 685 - 39.8 = 645.2\)
- Upper bound: \(\mu + \sigma = 685 + 39.8 = 724.8\)
So, the range that includes approximately 68% of the data is between 645.2 and 724.8.
Looking at the provided options:
1) between 656.2 and 703.8
2) between 645.4 and 724.8
3) between 565.6 and 804.4
4) between 605.4 and 764.6
The correct answer is **2) between 645.4 and 724.8**. Note that 645.4 is very close to the calculated lower bound 645.2, making it a suitable approximation.