Question

In the exercise, X is a binomial variable with n = 9 and p = 0.3. Compute the given probability. Check your answer using technology. HINT [See Example 2.] (Round your answer to five decimal places.) P(X = 5)

Answer 1

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

$P(X=r)=^nC_rp^rq^{n-r},~~\textup{where }q=1-p.$

According to the given information, we have

n = 9,  p = 0.3   and   q = 1 - p = 1 - 0.3 = 0.7.

Therefore, we get

$P(X=5)\\\\=^9C_5(0.3)^5(0.7)^{9-5}\\\\\\=\dfrac{9!}{5!(9-5)!}(0.3)^5(0.7)^4\\\\\\=\dfrac{9\times8\times7\times6\times5!}{5!\times4\times3\times2\times1}\times0.00273\times.2401\\\\=126\times0.000583443\\\\=0.073513818.$

Rounding to five decimal places, we get

P(X=5) = 0.07351.

Thus, the required probability is 0.07351.