Answer: The probability that no more than 6 of the 7 do not enjoy sports = 0.9999.
Step-by-step explanation:
Given : The proportion of people enjoy sports : p= 0.75
So , the proportion of people doesn't enjoy sports = 1-0.75=0.25
Let the random variable X be the number who doesn't enjoy .
Total number of people randomly selected : n= 7
Using Binomial distribution , the probability of getting x success :
[tex]P(X)=^nC_xp^x(1-p)^{n-x}[/tex] , n= Number of trails , p= Probability of getting success in each trial.
The probability that no more than 6 of the 7 do not enjoy sports :
[tex]P(X)=[tex]P(x\leq6)=1-P(x<6)\\\\=1-P(x=7)\\\\=1-^{7}C_7(0.25)^7(1-0.25)^{0}\\\\=1-(1)(0.25)^7\\\\=1-0.00006103515625=0.999938964844\approx0.9999[/tex]
Hence, the probability that no more than 6 of the 7 do not enjoy sports = 0.9999 .
