23.03.2023 - 16:16

The probability that an employee will be late to work at a large corporation is 0.21. What is the probability on a given day that in a department of 5 employees at least 3 are late?

Question:

The probability that an employee will be late to work at a large corporation is 0.21. What is the probability on a given day that in a department of 5 employees at least 3 are late?

Answers (1)
  • Vera
    April 18, 2023 в 18:32
    To solve this problem, we can use the binomial distribution formula. Let X be the number of employees that are late in a department of 5 employees. Then X follows a binomial distribution with n = 5 and p = 0.21. The probability that at least 3 employees are late can be calculated as follows: P(X ? 3) = P(X = 3) + P(X = 4) + P(X = 5) = (5 choose 3) * 0.21^3 * (1 - 0.21)^2 + (5 choose 4) * 0.21^4 * (1 - 0.21)^1 + (5 choose 5) * 0.21^5 * (1 - 0.21)^0 = 0.291 + 0.088 + 0.008 = 0.387 Therefore, the probability on a given day that in a department of 5 employees at least 3 are late is 0.387 or 38.7%.
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