Answer :
Final answer:
The mean of the research capacity can be calculated by adding up the time values of the 10 batteries and then dividing by 10. However, this is a sample mean that estimates the population mean. The accuracy of the estimate increases when samples are repeated and means averaged.
Explanation:
To calculate the mean of the research capacity in the population from a sample, you start by adding up the values of all the items in the sample, and then divide by the sample size. Since the question indicates we're dealing with 10 randomly selected automotive batteries, we'll assume that the total research time for these batteries is already given. If the total research time of the 10 batteries was say 600 hours, the sample mean will be 600 divided by 10, resulting in a mean of 60 hours.
However, please understand that this is the sample mean and may not be exactly equal to the population mean. But in statistics, when we assume that the sample is taken from a normally distributed population, we often treat the sample mean as an estimate for the population mean. This concept is derived from the Central Limit Theorem, which states that if we took repeated samples, the sample mean would equal the population mean in approximately 90 percent of the samples.
Note that it's also important to consider whether there are any outliers in your sample. An outlier can significantly shift your mean and provide a misleading representation of the typical value in your population. Sampling multiple times and averaging the recorded means could potentially strengthen the estimation.
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