Question

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Explanation:

Identify the given parameters

Using the Binomial Probability Distribution knowledge point

$$
LATEXBLOCK0
$$

Apply the binomial formula

Using the Binomial Probability Distribution knowledge point

$$ P(x) = \binom{n}{x} p^x q^{n-x} $$

Calculate the combination

Using the Binomial Probability Distribution knowledge point

$$ \binom{5}{4} = \frac{5!}{4!(5-4)!} = 5 $$

Compute the probability value

Using the Binomial Probability Distribution knowledge point

$$
LATEXBLOCK1
$$

Round to three decimal places

Using the Binomial Probability Distribution knowledge point

$$ P(x = 4) \approx 0.028 $$

Answer:

Let \(x\) be a binomial random variable with \(n = 5\), \(p = 0.3\). Find the following value. (Round your answer to three decimal places.)

\(P(x = 4) =\) <blank>0.028</blank>