Answer to Question #115803 in Statistics and Probability for Seifu

Question

The age of workers of an industry is normally distributed with mean 35 years and standard deviation of 5 years.
i) What is the probability that a randomly selected worker is
a) Less than 40 years of age
b) Between 28 and 37 years of age
c) At least 42 years of age
ii) Find the age
A) Below which 80% of workers have it
B) Above which 60% of workers have it

Answer 1

1)

a)P(x<40)

z=(x-μ)/σ=(40-35)/5=1

using table P(x<40)=0.8413=84.13%

b)P(28<x<37)=P(x<37)-P(x<28)

P(x<37)

z=(37-35)/5=0.4

using table P(x<37)=0.6554

P(x<28)

z=(28-35)/5=-1.4

using table P(x<28)=0.0807

P(28<x<37)=0.6554-0.0807=0.5747=57.47%

c) P(x≥42)=1-P(x<42)

z=(42-35)/5=1.4

using table P(x<42)=0.9192

P(x≥42)=1-0.9192=0.0808=8.08%

2)

a)P(x<X)=0.8

z-value(0.8)=0.84

z=(x-μ)/σ;

x=zσ+μ=0.84*5+35=39.2

b)P(x>X)=0.6

1-P(x<X)=0.6

P(x<X)=0.4

z-value(0.4)=-0.25

x=zσ+μ=-0.25*5+35=33.75