Question

1.(Binomial Distribution)Telephone manufacturers now offer 1000 different choices for a telephone (as combinations of color, type, options, portability, etc.). A company is opening a large regional office, and each of its 200 managers is allowed to order his or her own choice of a telephone. Assuming independence of choices and that each of the 1000 choices is equally likely, what is the probability that a particular choice will be made by none, one, two, or three of the managers?

Answer 1

Given: $n=200, p=1/1000=0.001, \mu=np=0.2$

So,

 $P(0)=\frac {0.2^0e^{-0.2}}{0!}=0.8187$

$P(1)=\frac {0.2^1e^{-0.2}}{1!}=0.1637$

$P(2)=\frac {0.2^2e^{-0.2}}{2!}=0.0164$

$P(3)=\frac {0.2^3e^{-0.2}}{3!}=0.0011$