Respuesta :
The number of trials and the probability of obtaining success will be given as P(X ≤ 2) = 0.9728.
How to find that a given condition can be modeled by binomial distribution?
Binomial distributions consist of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as
X \sim B(n,p)
The probability that out of n trials, there'd be x successes is given by
[tex]\rm P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
Assume the random variable X has a binomial distribution with the given probability of obtaining success.
Then the number of trials and the probability of obtaining success will be
P(X ≤ 2), n = 4, p = 0.2
Then we get
[tex]\rm P(X =2) = \: ^4C_2(0.2)^2(1-0.2)^{4-2}\\\\P (X=2) = 6 \times 0.0256 \\\\P (X=2) = 0.1536[/tex]
Then the cumulative probability will be
[tex]\rm P(X\leq 2) = 0.9728[/tex]
Learn more about binomial distribution here:
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