Question

Please show all work and complete all steps for ex.1

To illustrate, let us use the continuity correction and normal approximation to f ind POX- n- 20, p- 0.3). Converting to z values, we have (8+0.5)-6-2.5= (20)(0.3)(0.7) 2.0S 1.22 Example 1: Assume that x is a binomial random variable with n 100 and p 0.40. Use a normal approximation to find the following: a. P(x s 45) d. P(x 45) b. P(40 xS 50) e. P(x >45) c. P(x 2 38) f. P(x <45) H np (100)(4)-40 d» np(1-p)" (100)(.4)(6) σ 4.8989794 24 Binomial Normal a. P(x S 45) 0.8689 Plz s (45+.5-40)/4.8989794 )-P(25 i12) 5.3686 .8686 b. P(40 S x S 50) = P(S 50)-P(x P(39.5-40/4.8989794 sz s (50.5-40)/4.8989794) 39) - P(-0.1 sz s2.14) 0.9832-0.4621 -0.5211 .4838 + 0.0398 -0.5236 * You may finish questions (c) through (1) using the following rules of thumb. Rules of thumb Value being determined Correction -0.50 +0.50 -0.50 +0.50 0.50 and +0.50 +0.50 and -0.50 -0.50 and +0.50 x ? **P(2-χ < 4)--Let us break this into several parts First, x > 2 = reexpress to x 23 and, then, minus .5-x22.5 Second, x <仁reexpress to x 3 and, then, add-s-x 3.5 Finally, we get P( 2.5 sx s3.5)

Answer 1

Solution:

You as r ω'th ,n, ท. and : o.yo 6'y.ma/ ramolew? usin, ^1ь γ ma/ en app,.xm a-Hom 485HY sa table 0. 8686 . le

= 1-p( x-36) 62 4.8939 71 anple fol aler erma is k 0.86 86 nsst 0 6212 1-0.8212 : 0.176B、 Am. 4.8959 2 8212

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