Answer :
To solve this problem, we need to find the range that covers 68% of the students' weights, given that the weights are normally distributed with a mean of 140 pounds and a standard deviation of 16 pounds.
1. Understand the Normal Distribution:
- A normal distribution is symmetric around the mean. In this case, the mean is 140 pounds.
- The standard deviation, which measures the spread of the distribution, is 16 pounds.
2. 68% Range in Normal Distribution:
- In a normal distribution, approximately 68% of the data falls within one standard deviation from the mean. This range is one standard deviation below the mean to one standard deviation above the mean.
3. Calculate the Range:
- To find the lower bound, subtract the standard deviation from the mean:
140 pounds - 16 pounds = 124 pounds.
- To find the upper bound, add the standard deviation to the mean:
140 pounds + 16 pounds = 156 pounds.
Thus, the range that covers approximately 68% of the student weights is from 124 pounds to 156 pounds.
The correct answer is option A: 124 to 156 pounds.
1. Understand the Normal Distribution:
- A normal distribution is symmetric around the mean. In this case, the mean is 140 pounds.
- The standard deviation, which measures the spread of the distribution, is 16 pounds.
2. 68% Range in Normal Distribution:
- In a normal distribution, approximately 68% of the data falls within one standard deviation from the mean. This range is one standard deviation below the mean to one standard deviation above the mean.
3. Calculate the Range:
- To find the lower bound, subtract the standard deviation from the mean:
140 pounds - 16 pounds = 124 pounds.
- To find the upper bound, add the standard deviation to the mean:
140 pounds + 16 pounds = 156 pounds.
Thus, the range that covers approximately 68% of the student weights is from 124 pounds to 156 pounds.
The correct answer is option A: 124 to 156 pounds.
