Question 1203846

{{{ P(X<5)}}}, {{{ n=7}}}, {{{ p=0.3}}}

What is binomial distribution?
In binomial distribution for number trials we are investigating the probability of getting a success remain the same.


{{{ n }}}= number of trails,
{{{ p}}} = probability of success
{{{ x}}} = the number of success

given that {{{ P(x<5)}}}, so use {{{ x}}}={{{0}}},{{{1}}},{{{2}}},{{{3}}},{{{4}}}


{{{ p(x<5)=p(x=0)+p(x=1)+ p(x=2)+p(x=3)+p(x=4)}}}

{{{ p(x<5)=C(7,0)(0.3)^0(1-0.3)^7+C(7,1)(0.3)^1(1-0.3)^6+C(7,2)(0.3)^2(1-0.3)^5+C(7,3)(0.3)^3(1-0.3)^4+C(7,4)(0.3)^4(1-0.3)^3}}}

{{{ p(x<5)=0.0823543+0.2470629+0.3176523+0.2268945+0.0972405}}}

{{{ p(x<5)=0.9712045}}}
{{{ p(x<5)=0.9712}}}