It has been projected that the average and standard deviation of the amount of time spent online using the Internet are, respectively, 14 and 17 hours per person per year (many do not use the Internet at all!). a What value is exactly 1 standard deviation below the mean? b If the amount of time spent online using the Internet is approximately normally distributed, what proportion of the users spend an amount of time online that is less than the value you found in part (a)? (Is there a way to solve this and not use the standard normal table? If so, please explain.
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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It has been projected that the average and standard deviation of the amount of time spent online using the Internet are, respectively, 14 and 17 hours per person per year (many do not use the Internet at all!).
a What value is exactly 1 standard deviation below the mean?b If the amount of time spent online using the Internet is approximately
normally distributed , what proportion of the users spend an amount of time online that is less than the value you found in part (a)? (Is there a way to solve this and not use the standard normal table? If so, please explain.
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