Ask Question
15 July, 10:16

A corporation has 11 manufacturing plants. Of these, seven are domestic and four are outside the United States. Each year a performance evaluation is conducted for four randomly selected plants. What is the probability that a performance evaluation will include at least one plant outside the United States

+2
Answers (1)
  1. 15 July, 10:39
    0
    The probability that a performance evaluation will include at least one plant outside the United States is 0.836.

    Step-by-step explanation:

    Total plants = 11

    Domestic plants = 7

    Outside the US plants = 4

    Suppose X is the number of plants outside the US which are selected for the performance evaluation. We need to compute the probability that at least 1 out of the 4 plants selected are outside the United States i. e. P (X≥1). To compute this, we will use the binomial distribution formula:

    P (X=x) = ⁿCₓ pˣ qⁿ⁻ˣ

    where n = total no. of trials

    x = no. of successful trials

    p = probability of success

    q = probability of failure

    Here we have n=4, p=4/11 and q=7/11

    P (X≥1) = 1 - P (X<1)

    = 1 - P (X=0)

    = 1 - ⁴C₀ * (4/11) ⁰ * (7/11) ⁴⁻⁰

    = 1 - 0.16399

    P (X≥1) = 0.836

    The probability that a performance evaluation will include at least one plant outside the United States is 0.836.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “A corporation has 11 manufacturing plants. Of these, seven are domestic and four are outside the United States. Each year a performance ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers