The probability that a randomly selected teenager watched a rented video at least once during a week was 0.75. What is the probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week? (Round your answer to four decimal places.)P(X greaterthanorequalto 5) = __.

Answer:0.7564Step-by-step explanation:Let X be the event of watching a rented video at least once during a week,Given,The probability of watching a rented video at least once during a week was, p = 0.75,So, the probability of not watching a rented video at least once during a week was, q = 1 - p = 0.25,Binomial distributive formula,[tex]P(x)=^nC_x p^x q^{n-x}[/tex]Where,[tex]^nC_x=\frac{n!}{x!(n-x)!}[/tex]Hence, the probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week,P(X ≥ 5) = P(X=5) + P(X=6 )+ P(X=7)[tex]=^7C_5 0.75^5 0.25^{7-5}+^7C_6 0.75^6 0.25^{7-6}+^7C_7 0.75^7 0.25^{7-7}[/tex][tex]=21 (0.75)^5 (0.25)^2 + 7 (0.75)^6 0.25 + 0.75^7[/tex][tex]=0.756408691406[/tex][tex]\approx 0.7564[/tex]