Answer :
The probability of x<4 successes is P(X <4) = 0.01909.
How to find that a given condition can be modelled by binomial distribution?
Binomial distributions consist of n independent Bernoulli trials.
Bernoulli trials are those trials that 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 binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
In this question:
n=10 p=0.15 x<4
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\\\\\\P(X < 4) = \: ^{10}C_40.15^4(1-0.15)^{10-4}\\\\\\P(X < 4) = \: ^{10}C_40.00050625(0.85)^{6}\\\\\\P(X < 4) = 0.01909[/tex]
So, P(X <4) = 0.01909.
Learn more about binomial distribution here:
https://brainly.com/question/13609688
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