7. The campus bookstore sells on average 6 shirts per hour What is the probabili

Question

7. The campus bookstore sells on average 6 shirts per hour What is the probability that they sell 4 shirts in one hour? (5) a. b. What is the probability that they sell 8 shirts in 3 hours? (5) What is the appropriate distribution to model this problem? (2) c. 8. You volunteer to be in charge of ordering shirts for Camp War Eagle for next summer. The person who was in charge last year gives you the following information about the distribution of shirt orders from 2017, where X is the number of shirts that might have been needed in 2017. E[X] = 5,500 Var(X) = 2,500 After meeting with the admissions office, you conclude that the number of shirts needed for next year is 1.5 times higher than what you needed last year, and you are going to order an extra 300 shirts on top of that. Let Y be the number of shirts that you might need for Camp War Eagle in 2018. a. Write and expression relating X and Y (write Y in terms of X). (2) b. What is E[Y]? (2) c. What is Var[Y]? (2) d. What is E[Y21 (2)

Explanation / Answer

Ans:

7)

c)Poisson distribution with mean=6 shirts per hour

a)P(x=4)=e-6*(64/4!)=0.1339

or use excel function POISSON:

P(x=4)=POISSON(4,6,FALSE)=0.1339

b)Mean=6 shirt per hr=18 shirts per 3 hrs

P(x=8)=e-18*(188/8!)=0.0042

8)E[X]=5500,Var(Y)=2500

a)Y=1.5X+300

b)E[Y]=1.5E[X]+300=1.5*5500+300=8550

c)Var(Y)=1.52*Var(X)=2.25*2500=5625

d)Var(Y)=E[Y2]-E[Y]2

5625=E[Y2]-85502

E[Y2]=73108125

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

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