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Assume that a procedure yields a binomial distribution with a trial repeated n = 20 times. Use either the binomial probability formula (or technology) to find the probability of k = 14 successes given the probability p = 0.72 of success on a single trial.

Respuesta :

Answer:

the probability is 0.1879

Step-by-step explanation:

If a procedure yields a binomial distribution, the probability of having k successes is given by:

[tex]P(k)=nCk*p^{k} *(1-p)^{n-k}[/tex]

Where nCk is calculated as:

[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]

Additionally, n is the number of trials and p is the probability of success in every trial.

Replacing, k by 14, n by 20 and p by 0.72 we get:

[tex]20C14=\frac{20!}{14!(20-14)!}=38,760[/tex]

[tex]P(k)=20C14*0.72^{14} *(1-0.72)^{20-14}[/tex]

[tex]P(k)=38,760*0.72^{14} *(1-0.72)^{20-14}\\P(k)=0.1879[/tex]

So, the probability is 0.1879

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