Question

1. You're asked to settle a dispute about someone's chances of winning the lottery. There are 40 numbers to pick from (1 through 40). A sample of 6 is drawn but arrangement (order of a winning number being drawn) is not important. if someone buys only one ticket, what are his/her chances of winning? What if he/she buys two tickets? (5 points 2. Which control chart is best suited for each of the following situations and why? (10 points) (Xbar-R, I-MR, P, NP, C, or U) Tracking number of errors made on a loan application Measuring the inner diameter of a bottle cap in high-volume production Tracking the rate of defective units found during 100% incoming inspection Verifying the prying force required to separate two bonded surfaces (product becomes a. b. c. d. unusable after test) e. Tracking the rate or number of students showing up late to class. 3, A finite lot of 30 bicycles has 10% designated nonconforming for gear problems. What is the probability that a sample of 5 bikes has 2 bikes with the gear problem? (5 points) 4. A washer front panel is checked for surface defects after the paint operation. This process has been averaging 2.4 defects per panel. What is the probability that the next panel checked is perfect (no defects)? (5 points)

Question 1&2

Answer 1

Question 1

A sample of 6 numbers can be drawn from 1 to 40 without arrangement in

/40 ways 6

Since arrangement is not a criteria to win, then pertaining to the same ticket number, there can be 6*5*4*3*2*1 = 6! winning combinations.

Thus, probability of winning the lottery by buying 1 ticket =

6! (67 way

If a person buys 2 tickets, then the required probability of winning is defined as follows,
P(A) + P(B), where A denotes the event of winning from 1st ticket whereas B denotes the event of winning given A did not occur.

6! 40 6


6! 6!

Required Probability of winning with 2 lottery tickets = P(A) + P(B)

Question 2

a. Tracking number of errors made on a loan application : this describes a discrete data with multiple defects per unit for constant sample size : Thus we shall use a C Chart

b. Measuring the inner diameter of a bottle cap in a high volume production : this describes a continuous data measurement with high sampling number: Thus we shall use a Xbar-S Chart

c. Tracking the rate of defective units found during 100% incoming inspection : Discrete data with constant sample size - NP Chart

d. Verifying the prying force required to separate two bonded surfaces : Continuous data with varying sample size - U Chart

e. Tracking the rate of number of students coming late to class : Discrete data with varying sample size - P chart