Respuesta :
Answer:
[tex] P(X=8)[/tex]
And using the probability mass function we got:
[tex]P(X=8)=(20C8)(0.58)^8 (1-0.58)^{20-8}=0.0486[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=20, p=1-0.42=0.58)[/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]
And we want to find this probability:
[tex] P(X=8)[/tex]
And using the probability mass function we got:
[tex]P(X=8)=(20C8)(0.58)^8 (1-0.58)^{20-8}=0.0486[/tex]
The probability of exactly eight successful trials is 0.0486 and this can be determined by using the formula of the probability mass function.
Given :
- A random variable X counts the number of successes in 20 independent trials.
- The probability that any one trial is unsuccessful is 0.42.
According to the binomial distribution, the probability mass function is given by:
[tex]\rm P(X) = \; (^nC_x )(p^x)(1-p)^{n-x}[/tex]
where the value of n is 20 and the value of (p = 1 - 0.42 = 0.58).
Now, substitute the values of known terms in the above expression of probability mass function.
[tex]\rm P(X=8) = \; (^{20}C_8 )((0.58)^8)(1-0.58)^{20-8}[/tex]
Simplify the above expression in order to determine the probability of exactly eight successful trials.
P(X = 8) = 0.0486
For more information, refer to the link given below:
https://brainly.com/question/23017717
