IND508 OPERATIONS RESEARCH I

ECMB11H3Y Quantitative Methods in Economics I L01

Lecture 05In Class ExerciseProblem 1The probability that a customer entering a clothing store will make a purchase is 0.3.

(a) If 3 people walk into the store, what is prob. 2 will buy something?(b) Construct a tree diagram to answer (a)Problem 2The student body of a large university consists of 60% female students. In a random sample of 8 students, what is the probability that exactly two are female? Problem 3x is a Binomial random variable iwht n = 10 and p = .10.

(a) Find P(x 2)

(b) What is the expected value and standard deviation of x?Problem 4Average # of cars arriving at ATM machine in a 15min period is 10. Assume # of cars arriving is Poisson Distributed random variable.(a) What is prob. 5 cars arrive Monday 9a 9:15am?(b) What is prob. 5 cars arriving Monday 9-10am?

(c) What is prob. There will be 2 cars or less arriving Monday 9 9:15am?

(d) What is prob. more than 2 cars arriving Monday 9-9:15am?

(e) What is expected number of cars arriving Monday 9 9:30am?

(f) What is prob. 5 cars arriving at 10-10:15am and 5 cars arriving 10:15-10:30am?

(g) Given 30 cars arrived Monday 9-9:15am, what is prob. 5 cars arrive 9:15 9:30am?

Problem 5During the period of time that a doctors office takes phone-in bookings, calls come in at the rate of one every four minutes. What is the probability of 2 calls in 5 minutes?

Problem 6Shelly removed 2 dead batteries from flash light and mixed them up with 2 new ones. If she pick up 2 of them randomly, what is prob. both are good?Problem 7A company packs 12 electric fuses in a box. An inspector selects 3 units from the box for testing. Suppose the box contains 5 defects. (a) What is prob. that one of the 3 selected is a defective?

(b) What is probability there will be at least one defect found?

(c) What is expected number of defects found? Standard Deviation?(d) What is probability of getting one defect if the box contains 1000 fuses instead of just 12?1