2. x 45678

3. For every x 1. 0 ≤ P(x) ≤ 1 2. ∑P(x)=1 #defects01234 p(x)0.030.240.460.08?

4. #defects01234 p(x)0.030.240.460.080.19 Mean = St. Dev = (Expected Value) (L 1 -2.16) 2 x L 2 Calculator

5. #defects01234 p(x)0.030.240.460.080.19

6. Linear Function: Mean of Variance of

7. Properties: 1.Fixed # of trials 2. Each trial results in 1 of 2 outcomes 3. Outcomes of different trials are independent 4. P(x) remains the same

8. Y N Y N Y N Y N Y Y N N Y N Prob. Dist of Yes’s on survey YYYNYY YYNNYN NYYNNY NYNNNN

9. # yes’sP(x) 01230123 *remember Pascal’s triangle? Calculator:P(x=2): binompdf(3,.6, 2) = 0.432 P(x<2): binomcdf(3,.6, 1) = 0.352 P(x>2): 1 - binomcdf(3,.5, 2) = 0.216

10. Mean: St. Dev: Given: total number – n Probability Ask: Exactly x At least x More than x

11. Example: The probability that a certain machine will produce a defective item is 0.20. If a random sample of 6 items is taken from the output of this machine, what is the probability that there will be more than 4 defective items in this sample? 1-binomcdf(6,0.2, 4) = 0.0016 At least 2 items? 1-binomcdf(6, 0.2, 1)=0.34464

12. “Go Until” The probability that a person will wear glasses is 0.30. What is the probability that exactly 3 people must be picked before one with glasses is included in the sample? Calculator: Geompdf(0.3, 3)

14. Standard Normal: (called the z – curve) Calculator: Use normalcdf (beginning, end, mean, st. dev) Use to Find Probability To Find a Value Calculator: Use invnorm (%, mean, st. dev)

15. Example: IQ scores are normally distributed with a mean of 100 and a st. dev. of 15. What is the probability that you select a student at random with an IQ greater than 120? What is the IQ score associated with the 25 th percentile? Normcdf (120,∞,100,15) = 0.09 Invnorm (.25, 100,15)= 89

16. Example: Find the mean and standard deviation of normally distributed data if 27.7% is less than 18 and 33.3% is greater than 27. 1827

17. Properties for Mean: 1. 2. 3.If population is normal – then sampling distribution is approx. normal 4. Central Limit Theorem – if n is large enough, its approx normal Properties for Proportion: 1. 2. 3. Approx. normal if: An n increasesdecreases