Question

Question was provided via image upload.

Explanation:

Identify the parameters and target probability

Using the Binomial Probability Distribution knowledge point
We are given a binomial random variable \(x\) with parameters:

• Number of trials: \(n = 7\)
• Probability of success: \(p = 0.8\)
• Probability of failure: \(q = 1 - p = 0.2\)

We need to evaluate the probability:

$$ P(3 \le x \le 4) = P(x = 3) + P(x = 4) $$

Calculate the individual probability \(P(x = 3)\)

Using the Binomial Probability Distribution knowledge point

$$
LATEXBLOCK0
$$

Calculate the individual probability \(P(x = 4)\)

Using the Binomial Probability Distribution knowledge point

$$
LATEXBLOCK1
$$

Sum the probabilities and round

Using the Binomial Probability Distribution knowledge point

$$
LATEXBLOCK2
$$

Rounding to three decimal places gives \(0.143\).

Answer:

Consider a binomial random variable with \(n = 7\) and \(p = 0.8\). Let \(x\) be the number of successes in the sample. Evaluate the probability. (Round your answer to three decimal places.)

\(P(3 \le x \le 4) =\) <blank>0.143</blank>