30.To see if young men ages 8 through 17 years spend more or less time than the national average of $24.50 per shopping trip to a local mall, the manager surveyed 23 young men and found the average amount spent was $26.70. The standard deviation of the sample was $3.50. At a = 0.02, can it be concluded that the average spent at the local mall is more than the national average of $24.50?
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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