Respuesta :
Answer: The required probability is 0.07351.
Step-by-step explanation: Given that X is a binomial variable with n = 9 and p = 0.3.
We are given to compute the probability P(X = 5) and round the answer to five decimal places.
We know that
the binomial distribution formula for P(X = r) with n number of trials is given by
[tex]P(X=r)=^nC_rp^rq^{n-r},~~\textup{where }q=1-p.[/tex]
According to the given information, we have
n = 9, p = 0.3 and q = 1 - p = 1 - 0.3 = 0.7.
Therefore, we get
[tex]P(X=5)\\\\=^9C_5(0.3)^5(0.7)^{9-5}\\\\\\=\dfrac{9!}{5!(9-5)!}(0.3)^5(0.7)^4\\\\\\=\dfrac{9\times8\times7\times6\times5!}{5!\times4\times3\times2\times1}\times0.00273\times.2401\\\\=126\times0.000583443\\\\=0.073513818.[/tex]
Rounding to five decimal places, we get
P(X=5) = 0.07351.
Thus, the required probability is 0.07351.
