Question

A random sample of n=100 observations is selected from a population with μ=31and sigma equals 25σ=25.

Approximate the probabilities shown below.

a. ​ P(x overbarxgreater than or equals≥​28)	b. ​ P(22.1less than or equals≤x overbarxless than or equals≤​26.8)
c. ​ P(x overbarxless than or equals≤​28.2)	d. ​ P(x overbarxgreater than or equals≥​27.0)

a.

​ P(x overbarxgreater than or equals≥​28)equals=3880.573880.57 ​(Round to three decimal places as​ needed.)

answer a is correct- need b, c , and d.

Answer 1

Note that sample mean X follows a Normal distribution with Mean = μ-31 Standard deviation-o/vn-2.5 Note that z (x-H)/(o/Vn) - (x31)/2.5 -(Eq.1) follows standard Normal. when x-28, from (Eq.1) , z =-1.2 P(X > 28)-P(Ζ >-1.2)-1-P(Z <-12):1-0. 1 1 51-0885 (ans) When R 22.1, from (Eq.1),z- -3.56 When R 26.8, from (Eq.1),z--1.68 P(22.1 < X < 268)-P(-3.56 < Z <-1.68-P(Z <-1.68)-P(Z <-3.56)=0.0465-0.0002 = 0.046 When X 28.2, from (q.1), z-1.12 PO-28.2)-P(Z<-1.12)-0.131 (ans) when x = 27, from (Eq.1) , z =-1.6 PX> 27)-P(Z -1.6)-1-P(Z-1.6)-1-0.0548-0.945 (ans) (ans)