A report in 2010 indicates that Americans between the ages of 8 and 18 spend an average of μ = 7.5 hours per day using some sort of electronic device such as smart phones, computers, or tablets. Assume that the distribution of times is normal with a standard devia- tion of σ = 2.5 hours and find the following values. What is the probability of selecting an individual who uses electronic devices more than 12 hours a day? What proportion of 8- to 18-year-old Americans spend between 5 and 10 hours per day using elec- tronic devices? In symbols, p(
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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A report in 2010 indicates that Americans between the ages of 8 and 18 spend an average of μ = 7.5 hours per day using some sort of electronic device such as smart phones, computers, or tablets. Assume that the distribution of times is normal with a standard devia- tion of σ = 2.5 hours and find the following values.
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What is the
probability of selecting an individual who uses electronic devices more than 12 hours a day? -
What proportion of 8- to 18-year-old Americans
spend between 5 and 10 hours per day using elec- tronic devices? In symbols, p(5 < X < 10) = ?
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