Answer :
Sure, let's solve this step-by-step.
We know the following information about the life spans of Brand X and Brand Y batteries:
- Brand X:
- Mean life span: 102 hours
- Standard deviation: 0.8 hours
- Brand Y:
- Mean life span: 100 hours
- Standard deviation: 14 hours
### Part 1: Brand X
We need to find the interval for which 68% of the batteries lie.
For a normal distribution, approximately 68% of the values lie within one standard deviation of the mean.
So for Brand X:
- Lower bound: mean - standard deviation = 102 - 0.8 = 101.2 hours
- Upper bound: mean + standard deviation = 102 + 0.8 = 102.8 hours
Therefore, about 68% of Brand X's batteries have a life span between 101.2 and 102.8 hours.
### Part 2: Brand Y
We need to find the interval for which 68% of the batteries lie for Brand Y as well.
Similarly, for Brand Y:
- Lower bound: mean - standard deviation = 100 - 14 = 86 hours
- Upper bound: mean + standard deviation = 100 + 14 = 114 hours
Therefore, about 68% of Brand Y's batteries have a life span between 86 and 114 hours.
### Part 3: Comparison
Finally, we compare the standard deviations to determine which brand's battery life span is more consistently close to the mean.
- Brand X standard deviation: 0.8 hours
- Brand Y standard deviation: 14 hours
Since Brand X has a smaller standard deviation than Brand Y, the life span of a Brand X battery is more likely to be consistently close to the mean.
### Final Answer
- About 68% of Brand X's batteries have a life span between 101.2 and 102.8 hours.
- About 68% of Brand Y's batteries have a life span between 86 and 114 hours.
- The life span of a Brand X battery is more likely to be consistently close to the mean.
We know the following information about the life spans of Brand X and Brand Y batteries:
- Brand X:
- Mean life span: 102 hours
- Standard deviation: 0.8 hours
- Brand Y:
- Mean life span: 100 hours
- Standard deviation: 14 hours
### Part 1: Brand X
We need to find the interval for which 68% of the batteries lie.
For a normal distribution, approximately 68% of the values lie within one standard deviation of the mean.
So for Brand X:
- Lower bound: mean - standard deviation = 102 - 0.8 = 101.2 hours
- Upper bound: mean + standard deviation = 102 + 0.8 = 102.8 hours
Therefore, about 68% of Brand X's batteries have a life span between 101.2 and 102.8 hours.
### Part 2: Brand Y
We need to find the interval for which 68% of the batteries lie for Brand Y as well.
Similarly, for Brand Y:
- Lower bound: mean - standard deviation = 100 - 14 = 86 hours
- Upper bound: mean + standard deviation = 100 + 14 = 114 hours
Therefore, about 68% of Brand Y's batteries have a life span between 86 and 114 hours.
### Part 3: Comparison
Finally, we compare the standard deviations to determine which brand's battery life span is more consistently close to the mean.
- Brand X standard deviation: 0.8 hours
- Brand Y standard deviation: 14 hours
Since Brand X has a smaller standard deviation than Brand Y, the life span of a Brand X battery is more likely to be consistently close to the mean.
### Final Answer
- About 68% of Brand X's batteries have a life span between 101.2 and 102.8 hours.
- About 68% of Brand Y's batteries have a life span between 86 and 114 hours.
- The life span of a Brand X battery is more likely to be consistently close to the mean.
