Answer to Question #115801 in Statistics and Probability for Seifu

Question

The salary of workers of an industry is normally distributed with mean salary of 420 Birr and standard deviation of 55 Birr. If any one worker from the industry is selected randomly,
i) What is the probability that he or she has salary of
a) More than 450 Birr
b) Less than 300 Birr
c) Between 380 and 490 Birr
ii) What is the salary
a) Below which 5% of workers have it
b) Above which 35% of workers have it

Answer 1

1)

a)P(x>450)=1-P(x<450)

P(x<450), z=(x-μ)/σ=(450-420)/55=0.54

using table P(x<450)=0.7054

P(x>450)=1-0.7054=0.2946=29.46%

b)P(x<300)

z=(300-420)/55=-2.18

using table P(x<300)=0.01463=1.46%

c)P(380<x<490)=P(x<490)-P(x<380)

P(x<490)

z=(490-420)/55=1.27

using table P(x<490)=0.898

P(x<380)

z=(380-420)/55=-0.73

using table P(x<380)=0.2327

P(380<x<490)=0.898-0.2327=0.6653=66.53%

2)

a)P(x<X)=0.05

z-value(0.05)=-1.64

z=(x-μ)/σ;

x=zσ+μ=-1.64*55+420=329.8

b)P(x>X)=0.35

1-P(x<X)=0.35

P(x<X)=0.65

z-value(0.65)=0.39

x=zσ+μ=0.39*55+420=441.45