Question

question 10 solve for x ~ b(10, 0.75) for x = 5. 0.06 0.09 0.23 0.52 1 pts

Explanation:

Step1: Recall binomial - probability formula

The binomial - probability formula is $P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}$, where $n$ is the number of trials, $k$ is the number of successes, $p$ is the probability of success on a single trial, and $C(n,k)=\frac{n!}{k!(n - k)!}$.

Step2: Identify values of $n$, $k$, and $p$

Here, $n = 10$, $k = 5$, and $p=0.75$. Then $1 - p = 0.25$.

Step3: Calculate the binomial coefficient $C(n,k)$

$C(10,5)=\frac{10!}{5!(10 - 5)!}=\frac{10!}{5!5!}=\frac{10\times9\times8\times7\times6}{5\times4\times3\times2\times1}=252$.

Step4: Calculate the probability

$P(X = 5)=C(10,5)\times(0.75)^{5}\times(0.25)^{10 - 5}$
$P(X = 5)=252\times(0.75)^{5}\times(0.25)^{5}$
$P(X = 5)=252\times0.2373046875\times0.0009765625\approx0.23$.

Answer:

0.23