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# normal distribution question

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

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A normal distribution question is emphasized.

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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 - ...

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