Problems 4.9, 4.12, 4.13, 4.20 from the attached tasks.

See the attached files.

4.9: this is a normal distribution question:

Let’s define: m=1000, S2 = 10000,

then the standard deviation is SD=SQRT(S2)=100

(a) by the formula: z = (X-m)/SD

z1 = (1200-1000)/100 = 2

from a z table, we find that Pr(z<2) = 0.9773

z2 = (800-1000)/100 = -2

Pr(z< -2) = 1- Pr(z<2) = 1-0.9773 = 0.0227

then Pr(800<x<1200) = Pr(-2<z<2)= Pr(z<2) – Pr(z< -2) = 0.9773-0.0227 = 0.9546

(b) As shown in (a), Pr(x>1200) = 1- Pr(x<1200) = 1- Pr(z<2) = 1-0.9773 = 0.0227

(c) As shown in (a), Pr(x<800) = Pr(z< -2) = 1- Pr(z<2) = 1-0.9773 = 0.0227

(d) z3 = (5000-1000)/100 =40

Obviously, Pr(z>40) = 1 – …

A normal distribution question is emphasized.