STAT 1000 Lecture Notes - Lecture 29: Central Limit Theorem, Binomial Distribution, Random Variable

• School: University of Manitoba
• Department: Statistics
• Course: STAT 1000
• Professor: Zenaida Mateo

Document Summary

The mean diameter of all bolts produced is known to be = Even though we don"t know the form of the distribution of diameters, since the sample size is high, we know that the distribution of x is approximately normal. P(1. 24 < < 1. 26) p(cid:4672)(cid:1005). (cid:1006)(cid:1008) (cid:1005). (cid:1006)(cid:1009) (cid:1004). (cid:1004)(cid:1009) (cid:1005)(cid:1004)(cid:1004)<< (cid:1005). (cid:1006)(cid:1010) (cid:1005). (cid:1006)(cid:1009) (cid:1004). (cid:1004)(cid:1009) (cid:1005)(cid:1004)(cid:1004)(cid:4673) = p( -2. 00 < z < 2. 00) = 0. 9544. We do(cid:374)"t k(cid:374)o(cid:449) the fo(cid:396)(cid:373) of the dist(cid:396)i(cid:271)utio(cid:374) of x, a(cid:374)d the sample size is not high enough to use the central limit theorem. In the previous unit you were introduced to the binomial distribution and the points that need to be satisfied in order for a variable to be considered binomial. I(cid:374) sa(cid:373)pli(cid:374)g (cid:449)e like to esti(cid:373)ate the p(cid:396)opo(cid:396)tio(cid:374) of (cid:862)su(cid:272)(cid:272)esses(cid:863) ou(cid:396) esti(cid:373)ato(cid:396) is: X is the count of successes, a binomial random variable. N is the size of the sample.