Respuesta :
Answer:
The probability that a performance evaluation will include at least one plant outside of the country is 0.76.
Step-by-step explanation:
The random variable X can be defined as the number of outside of the country plants that are selected for a performance evaluation.
A sample of n = 4 plants are selected each year for a performance evaluation.
The probability of selecting an outside of the country plant is, p = 0.30.
A plant selected can either be a domestic plant or outside of the country plant. They are not dependent on each other.
Thus, the random variable X follows a Binomial distribution with parameters n = 4 and p = 0.30.
The probability mass function of X is:
[tex]P(X=x)={4\choose x}\ 0.30^{x}(1-0.30)^{4-x};\ x=0,1,2,3...[/tex]
Compute the probability that a performance evaluation will include at least one plant outside of the country as follows:
P (X ≥ 1) = 1 - P (X < 1)
= 1 - P (X = 0)
[tex]=1-{4\choose 0}\ 0.30^{0}(1-0.30)^{4-0}\\\\=1-(1\times 1\times 0.2401)\\\\=1-0.2401\\\\=0.7599\\\\\approx 0.76[/tex]
Thus, the probability that a performance evaluation will include at least one plant outside of the country is 0.76.
