nts) in a certain population of voters, 72% of them plan to vote in favor of a newpiece of proposed legislation. If a random sample of 25 people is taken from thispopulation, find the probability that 10 of them plan to vote against this piece ofproposed legislation.​

Answer:Probability that 10 of them plan to vote against this piece of  proposed legislation is 0.0701 or 7.01 %.Step-by-step explanation:Consider the event of voting against the piece as success, 'p'. So, voting in favor of the piece is failure and denoted by 'q'.Given:Sample size is, [tex]n=25[/tex]Probability of failure is, [tex]q=72\%=0.72[/tex]Therefore, probability of success is, [tex]p=1-q=1-0.72=0.28[/tex]Number of successes is, [tex]x=10[/tex]Now, from Bernoulli's distribution, probability of [tex]x[/tex] successes out of [tex]n[/tex] samples is given as:[tex]P(X=x)=_{n}^{x}\textrm{C}p^xq^{n-x}[/tex]Here, [tex]n=25,x=10,p=0.28,q=0.72[/tex]. Therefore,[tex]P(X=10)=_{25}^{10}\textrm{C}(0.28)^{10}(0.72)^{25-10}\\P(X=10)=_{25}^{10}\textrm{C}(0.28)^{10}(0.72)^{15}\\P(X=10)=3.269\times 10^{6}\times 2.962\times 10^{-6}\times 7.244\times 10^{-3}\\P(X=10)=70.142\times 10^{-3}=0.0701=7.01\%[/tex]Therefore, probability that 10 of them plan to vote against this piece of  proposed legislation is 0.0701 or 7.01 %.