Question

nine plants are operated by a garment manufacturer. they feel there is a eighteen percent chance for a strike at any one plant and the risk of a strike at one plant is independent of the risk of a strike at another plant. let \\(x\\) be the number of plants of the garment manufacturer that strike.

step 2 of 3: compute the expected value of \\(x\\). round your answer to two decimal places, if necessary.

Explanation:

Identify the distribution parameters

The problem describes a scenario with a fixed number of independent trials, where each trial has only two possible outcomes (strike or no strike) with a constant probability of success. This fits a binomial distribution.

• Number of trials (plants), \(n = 9\)
• Probability of success (strike at any one plant), \(p = 18\% = 0.18\)
• Let \(X\) be the binomial random variable representing the number of plants that strike: \(X \sim \text{Binomial}(n = 9, p = 0.18)\).

Recall the expected value formula

For a binomial random variable \(X\), the expected value \(E[X]\) (or mean \(\mu\)) is calculated using the formula:

$$E[X] = n \cdot p$$

Calculate the expected value

Substitute the identified parameters into the formula:

$$E[X] = 9 \cdot 0.18$$

$$E[X] = 1.62$$

The value is already at two decimal places, so no further rounding is necessary.

Answer:

Compute the expected value of \(X\). Round your answer to two decimal places, if necessary. <blank>1.62</blank>