Drivers in Wyoming drive more miles yearly than motorists in any other state. The annual number of miles driven per licensed driver in Wyoming is 22,634 miles. Assume the standard deviation is 5,500 miles. A random sample of 250 licensed drivers in Wyoming is selected and the mean number of miles driven yearly for the sample is calculated. a. What value would we expect for the sample mean? b. What is the standard error for the sample mean? a. The expected sample mean is 22634 miles, because the sample mean is an unbiased estimator of the population mean. (Round to the nearest integer as needed.) b. What is the standard error for the sample mean? The standard error for the sample mean is miles. (Type an integer or decimal rounded to the nearest tenth as needed.)
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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