Respuesta :
Answer:
[tex]P(X=8)=(20C8)(0.74)^8 (1-0.74)^{20-8}=0.00108[/tex]
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Let X the random variable of interest, on this case we can assume that follows this distribution:
[tex]X \sim Binom(n=20, p=0.74)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Solution to the problem
For this case we want this probability:
[tex] P(X=8) [/tex]
And if we replace into the probability mass function we got:
[tex]P(X=8)=(20C8)(0.74)^8 (1-0.74)^{20-8}=0.00108[/tex]
The probability of getting 8 people selected is 0.00108.
The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either Success or Failure.
For example, if we toss a coin, there could be only two possible outcomes: heads or tails, and if any test is taken, then there could be only two results: pass or fail. This distribution is also called a binomial probability distribution.
There are two parameters n and p used here in a binomial distribution. The variable ‘n’ states the number of times the experiment runs and the variable ‘p’ tells the probability of any one outcome.
According to the question ;
Let X the random variable of interest, on this case we can assume that follows this distribution: x- Binomial ( n = 20 , p = 0.74 )
The probability mass function for the Binomial distribution is given as:
p(x) =( [tex]^nc\__x[/tex] ) [tex](p)^{x}[/tex] [tex]( 1-p)^{n-x}[/tex]
Where ([tex]^{n} c\__x[/tex]) means combinatory
For this case we want this probability:
P ( x = 8 ) =( [tex]^{20} c\__8[/tex]). [tex](0.74)^{8} (1-0.74)^{20-8}[/tex]
= 0.00108
The probability of 8 selected young adult is 0.00108.
For more information about probability distribution click the link given below
https://brainly.in/question/12324720
