MGEB11H3 Lecture Notes - Lecture 9: Binomial Distribution, Central Limit Theorem, Sampling Distribution

• School: UTSC
• Department: Economics for Management Studies
• Course: MGEB11H3
• Professor: Victor Yu

Document Summary

Mgeb11 lecture 9 chapter 6: continuous random variables: uniform distribution, normal distribution, let x~ n (m=100, sd=20); find p(80 < x < 125, let x~ n (m=100, sd=20) and k = constant. If p(75 < x < k) = 0. 4, k= : normal approximation to binomial probability. In chapter 5, we learned if x~binomial w/ n = # of indep. trials & p = p(success in each trail). The numerical answer is too difficult to find using a calculator so we will use a normal distribution bell-shape curve to approx. the numerical answer: in this example, n=200 and p=0. 2. Since x is binomial, mean of x = np = 200(0. 2) = 40. Variance of x = npq = 200(0. 2)(0. 8) = 32. In theory, p (cid:894)(cid:1007)5(cid:1004) < x <= (cid:1012)(cid:1004)(cid:1004)(cid:895) = p (cid:894)x = (cid:1007)5(cid:1005), (cid:1007)5(cid:1006) , (cid:1012)(cid:1004)(cid:1004)(cid:895) P (cid:894)(cid:1007)5(cid:1004) <= x < (cid:1012)(cid:1004)(cid:1004)(cid:895) = p (cid:894)x = (cid:1007)5(cid:1004), (cid:1007)5(cid:1005), ,(cid:1011)(cid:1013)(cid:1013)(cid:895) x = binomial.