Final answer:
The mean is the average of a set of values, and variance measures how spread out the values are around the mean. Standard deviation is used to compute variance by squaring it. In hypothesis testing, comparing means or assessing claims against empirical data is a common practice.
Step-by-step explanation:
The student's question revolves around statistical concepts like the mean, variance, hypothesis testing, probability distribution, and lifespan analysis in different contexts. To calculate the mean (average) of a dataset, add up all the numbers and then divide by the count of numbers. Variance measures the dispersion of a set of data points around their mean value. When the standard deviation is known, as in the case of tire lifespan and CD player lifespan, it can be used to calculate the variance by squaring the standard deviation. The test of lifespans in a county involves a test of means to compare average lifetimes between two groups. In hypothesis testing involving the survey of a tire's lifespan, we would consider whether the data is highly inconsistent with the claimed mean lifespan using a one-tailed test because we are only interested if the mean is less than the claim. For the lightbulb longevity, if the distribution is exponential, we can use the exponential probability density function to calculate relevant probabilities and determine the cutoff for the lowest two percent based on the given mean lifetime.