quantitive methods and lean manufacturing

1. What is the difference between discrete and continuous random variables?

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2. What are the meanings of: binomial, Poisson and exponential distributions?

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3. In a continuous distribution f(x) must be >___________ and the total area under the curve must equal ______________?

4. Explain the Empirical Rule for normal curves

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

5. Explain how a z score standardizes a distribution

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

6. F distributions test for differences in what?

________________________________________________________________________

7. What effect do degrees of freedom have on F distributions?

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Use Excel to solve:

8. A company makes cars. Probability of 0 defective cars is 10%; 2 defects is 30%; 4 defects is 25%; 5 defects is 25% and 8 defects is 10%. Using x p(x) to calculate variance, what is the expected number of defects at +/- 2 sigma.

9. A company is making soap. Every day a supervisor takes a random sample of n=10. The probability p(x) a soap sample is bad is 0.1. Using a binomial distribution, find what is the probability of r= 3,4 or 5 defective soaps?

10. Machine breakdowns occur randomly at an average rate (λ) of 2 per day. Using a Poisson distribution, what is the probability p(x) of observing x=3 breakdowns in a given day at the factory?

11. Suppose manufacturing time for a component is normally distributed with an average of 5 minutes & standard deviation of 1 min. What is the probability a part can be made in ≤ 2.5 min? What is the probability a part can be made in ≥2.5 min?

12. Your factory has 2 ways to make a product. The engineering manager is trying to determine if the variance in both processes is the same. 2 independent random samples of sizes n1 = 12 and n2 = 8 are pulled from two normally distributed populations. Measured sample variances are 10 and 18. Using F testing at 95% confidence, can your manager say the variances are the same?

13. In your factory a repaired part lasts 15 years. Using an exponential distribution, what is the probability the part will last less than 6 years?

14. Using the VizDataEffectivelyPractice File complete graphs for: StandardDeviation (Ch 2 Effective Data Visualization), BacktoBack1 (Ch 3 Effective Data Visualization), Slopegraph (Ch 3 Effective Data Visualization)