The Bureau of Labor Statistics’ American Time Use Survey showed that the amount of time spent using a computer for leisure varied greatly by age. Individuals age 75 and over averaged 0.30 hour (18 minutes) per day using a computer for leisure. Individuals ages 15 to 19 spend 1.0 hour per day using a computer for leisure. If these times follow an exponential distribution, find the proportion of each group that spends: a. Less than 14 minutes per day using a computer for leisure. (Round your answers to 4 decimal places.) how many proportion age75 and over: how many proportion age 15 to 19: b. More than 2 hours. (Round your answers to 4 decimal places.) how many proportion age75 and over: how many proportion age 15 to 19: c. Between 28 minutes and 84 minutes using a computer for leisure. (Round your answers to 4 decimal places.) how many proportion age75 and over: how many proportion age 15 to 19: d. Find the 28th percentile. Seventy-two percent spend more than what amount of time? (Round your answers to 2 decimal places.) amount of time for individuals ages 75 and over: amount of time for individuals ages 15 to 19:
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!
The Bureau of Labor Statistics’ American Time Use Survey showed that the amount of time spent using a computer for leisure varied greatly by age. Individuals age 75 and over averaged 0.30 hour (18 minutes) per day using a computer for leisure. Individuals ages 15 to 19 spend 1.0 hour per day using a computer for leisure. If these times follow an exponential distribution, find the proportion of each group that spends:
a. Less than 14 minutes per day using a computer for leisure. (Round your answers to 4 decimal places.)
b. More than 2 hours. (Round your answers to 4 decimal places.)
c. Between 28 minutes and 84 minutes using a computer for leisure. (Round your answers to 4 decimal places.)
d. Find the 28th percentile. Seventy-two percent spend more than what amount of time? (Round your answers to 2 decimal places.)
amount of time for individuals ages 75 and over:
amount of time for individuals ages 15 to 19:
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