Customers can replace 1, 2, 3, or 4 tires at a time for their vehicle at Tire Masters, a nationwide tire shop chain. For customers who have had their tires replaced at Tire Masters, the mean number of tires replaced is u= 2.75, with a standard deviation of o = 0.65. Suppose that we will take a random sample of n=8 tire replacement orders. (Each order gives the number of tires being replaced.) Let x represent the sample mean of the 8 tire replacement orders. Consider the sampling distribution of the sample mean x. Complete the following. Do not round any intermediate computations. Write your answers with two decimal places, rounding if needed. (a) Find (the mean of the sampling distribution of the sample mean). (b) Find o- (the standard deviation of the sampling distribution of the sample mean).
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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