Question 1137176
{{{P(X)=C(16,X)*(0.25)^X*(1-0.25)^(16-X)}}}
.
.
.
*[illustration b.JPG].
.
.
.
a) {{{P(4)=00.225}}}
.
.
b) Less than 2 would be 0 or 1,
{{{P(X<2)=P(0)+P(1)}}}
{{{P(X<2)=0.010+0.053}}}
{{{P(x<2)=0.063}}}
.
.
c) Highest probability occurs with {{{X=4}}}.
From another direction, for a binomial distribution,
{{{mu=n*P}}}
{{{mu=0.25*16}}}
{{{mu=4}}}
.
.
d) For a binomial distribution,
{{{sigma=sqrt(n*P*(1-P))}}}
{{{sigma=sqrt(16*(1/4)(3/4))}}}
{{{sigma=sqrt(3)}}}