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) = .00625 for α ≤ 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 a daily discretionary spending of $150 or more?

d. What is the probability that consumers in this group have a daily discretionary spending of $80 or less?