Question

eleven percent of u.s. employees who are late for work blame oversleeping. you randomly select four u.s. employees who are late for work and ask them whether they blame oversleeping. the random variable represents the number of u.s. employees who are late for work and blame oversleeping.
find the mean of the binomial distribution.
μ = .44 (round to the nearest hundredth as needed.)
find the variance of the binomial distribution.
σ² = □ (round to the nearest hundredth as needed.)

Explanation:

Step1: Identify the parameters of binomial distribution

For a binomial distribution \(X\sim B(n,p)\), where \(n = 4\) (number of trials, i.e., number of employees selected) and \(p=0.11\) (probability of success, i.e., probability that an employee is late for work and blames oversleeping)

Step2: Recall the formula for variance of binomial distribution

The formula for the variance of a binomial distribution is \(\sigma^{2}=np(1 - p)\)

Step3: Substitute the values into the formula

Substitute \(n = 4\) and \(p = 0.11\) into the formula:

$$
LATEXBLOCK0
$$

Answer:

\(0.39\)