A Gallup Daily Tracking Survey found that the mean daily discretionary spending

Question

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 5 the discretionary spending per day and assume that a uniform probability
density function applies with f (x) 5 .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?
d. What is the probability that consumers in this group have daily discretionary spending
of $80 or less?

Explanation / Answer

Ans:

f(x) = 1/(b-a), so b-a = 1/0.00625 = 160.
The mean is 136 = (b+a)/2, so b+a = 272.
Adding these two equations, we get 2b=432, so b=216 and a=216-160 = 56

(a, b) = (56, 216)

b)CDF is

P(X<=x)=(x-56)/(216-56)=(x-56)/160

P(100<=x<=200)=P(x<=200)-P(x<=100)=[(200-56)/160]-[(100-56)/160]=100/160=0.625

c)P(X>=150)=1-(150-56)/160=1-0.5875=0.4125

d)P(x<=80)=(80-56)/160=24/160=0.15

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.