Answer:
0.1168
Step-by-step explanation:
This is binomial distribution probability. The formula to solve this is:
[tex]P(x)=\frac{n!}{(n-x)!x!} p^x q^{n-x}[/tex]
Where
p is the probability of success [3/4 or 0.75]
q is the probability of failure [1 - 0.75 = 0.25]
n is total number [we choose 9 people, so n = 9]
x is what we are trying to find [here we want 5 people agreeing, so x = 5]
Putting the information into the formula, we calculate the probability:
[tex]P(x=5)=\frac{9!}{(9-5)!5!} (0.75)^{5} (0.25)^{9-5}\\P(x=5)=\frac{9!}{4!5!}(0.75)^{5} (0.25)^{4}\\P(x=5)=(126)(0.2373)(0.0039)\\P(x=5)=0.1168[/tex]
Hence, the probability is 0.1168
By applying binomial distribution we got that probability that exactly 5 out of 9 randomly selected people will agree with the statement "Three out of four people think most advertising seeks to persuade people to buy things they don't need or can't afford" is 0.1168
What is probability ?
Probability is chances of occurring of an event.
Here given that three out of four people think most advertising seeks to persuade people to buy things they don't need or can't afford. and we have to find that he probability that exactly 5 out of 9 randomly selected people will agree with this statement.
We can find this probability using binomial distribution
So
[tex]P(x)=\frac{n !}{(n-x) ! x !} p^{x} q^{n-x}[/tex]
Where
p = probability of success =3/4 = 0.75
q= probability of failure =1-p=1 - 0.75 = 0.25
n is total number= 9
Now
probability that exactly 5 out of 9 randomly selected people will agree with given statement can be calculated as
[tex]$\begin{aligned}&P(x=5)=\frac{9 !}{(9-5) ! 5 !}(0.75)^{5}(0.25)^{9-5} \\&P(x=5)=\frac{9 !}{45 !}(0.75)^{5}(0.25)^{4} \\&P(x=5)=(126)(0.2373)(0.0039) \\&P(x=5)=0.1168\end{aligned}$[/tex]
By applying binomial distribution we got that probability that exactly 5 out of 9 randomly selected people will agree with the statement "Three out of four people think most advertising seeks to persuade people to buy things they don't need or can't afford" is 0.1168
To learn more about probability visit : brainly.com/question/24756209
