22 The average age for licensed drivers in the country is u = 42.6 years with a standard deviation of o = 12. The distribution is approximately normal. a. A researcher obtained a sample of n = 25 drivers who received parking tickets. The average age for these drivers was M = 40.5. Is this a reasonable outcome of a sample of n = 25, or is the sample %3D mean very different from what would normally be expected? (Hint: Compute the z-score for the sample mean.) b. The same researcher also obtained a sample ofn= 12 drivers who received speeding tickets. The average age for this sample was M = 34.4. Is this a reasonable outcome for a sample of n = 16, or is the sample mean very different from what would usually be expected? (Again, compute the z-score for 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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