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Answer :
Final answer:
In statistics, the mean lifespan of the batteries is 62 and the standard deviation is 8.5. The margin of error at a 98% confidence interval is approximately 3.3 months, yielding a confidence interval of 58.7 to 65.3 months. We are 98% confident that the mean battery life lies between these two values.
Explanation:
The subject of this problem is in the field of statistics, particularly dealing with samples and confidence intervals. To determine the mean, you would need to add up all the values and divide by 30. After calculating, you would find the mean to be approximately 62 months.
To find the standard deviation, you would subtract each number from the mean, square the results, add those, divide by the count minus one, and finally, take the square root. Plugging in the numbers, this boils down to about 8.5.
Margin of error is calculated using the formula: critical value * standard deviation / sqrt(sample size). If we're looking for a 98% confidence interval, the critical value is approximately 2.33. Plugging the numbers in, you get a margin of error of about 3.3.
The confidence interval is determined by subtracting and adding the margin of error from/to the mean. Thus, your confidence interval is approximately (58.7, 65.3)
For d, it can be said that we are 98% confident that the mean battery life for the population lies between 58.7 and 65.3 months.
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