A Gallup Daily Tracking Survey found that the mean daily discretionary spending by Americans earning over $90,000 per year was $136 per day (USA Today, July 30, 2012). The discretionary spending excluded home purchases, vehicle purchases, and regular monthly bills. Let x = the discretionary spending per day and assume that a uniform probability density function applies with f (x) = 0.00625 for a ≤ x ≤ b. a. Find the values of a and b for the probability density function. b. What is the probability that consumers in this group have daily discretionary spending between $100 and $200? c. What is the probability that consumers in this group have daily discretionary spending of $150 or more?
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!
A Gallup Daily Tracking Survey found that the mean daily discretionary spending by Americans earning over $90,000 per year was $136 per day (USA Today, July 30, 2012). The discretionary spending excluded home purchases, vehicle purchases, and regular monthly bills. Let x = the discretionary spending per day and assume that a uniform probability density
a. Find the values of a and b for the probability density function.
b. What is the probability that consumers in this group have daily discretionary spending between $100 and $200?
c. What is the probability that consumers in this group have daily discretionary spending of $150 or more?
d. What is the probability that consumers in this group have daily discretionary spending of $80 or less?
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