Question

The average income of the residents of a particular community is your roll no *1000 and sd is your roll no *100:

(a) What is the probability that income of a person, selected at random, is more than average income?

(b) What is the probability that income of a person, selected at random, is between average income and average income +2000? 

(c) What is the probability that income of a person, selected at random, is bbetween average income+1000 and average income +2000?

(d) What is the probability that income of a person, selected at random, is less than average income +1000?

Answer 1

(a) $P(X>100)=P(Z>0)=0.5.$

(b) $P(1000<X<3000)=P(0<Z<\frac{3000-1000}{100}=P(0<Z<20)=0.5000.$

(c) $P(2000<X<3000)=P(\frac{2000-1000}{100}<Z<\frac{3000-1000}{100})=$

$P(10<Z<20)=0.0000.$

(d) $P(X<2000)=P(Z<\frac{2000-1000}{100})=P(Z<10)=1.0000.$