Question

A binomial probability experiment is conducted with the given para meters compute the probability of X successes in the n independent trials of the experimentRound two for decimal placesn=40 p=0.97 x= 38

Answer 1

When performing a binomial probability experiment the probability of having X succeses in n tries with a succes probability p is given by the following formula:

`P(X)=(n!)/(X!\cdot(n-X)!)\cdot p^X\cdot(1-p)^(n-X)`

Then in order to find the probability we just need to take n=40, p=0.97 and X=38:

`\begin{gathered} P(X)=(n!)/(X!\cdot(n-X)!)\cdot p^X\cdot(1-p)^(n-X) \\ P(38)=(40!)/(38!\cdot(40-38)!)\cdot0.97^(38)\cdot(1-0.97)^(40-38) \\ P(38)=(39\cdot40)/(2!)\cdot0.314\cdot0.03^2 \\ P(38)=780\cdot0.314\cdot0.0009 \\ P(38)=0.220428 \end{gathered}`

And if we round two decimal places we have that:

`P(38)=0.22`