Here are the essential concepts you must grasp in order to answer the question correctly.
Binomial Distribution
The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. In this context, a 'success' is defined as an employee having access to medical care benefits. The distribution is characterized by two parameters: the number of trials (n) and the probability of success (p).
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Probability Calculation
To find the probability of a specific number of successes in a binomial distribution, we use the binomial probability formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k). Here, 'n choose k' represents the number of ways to choose k successes from n trials, p is the probability of success, and (1-p) is the probability of failure. This formula allows us to calculate the likelihood of different outcomes.
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Cumulative Probability
Cumulative probability refers to the probability that a random variable takes on a value less than or equal to a certain threshold. In this case, to find the probability that more than six employees have access to medical care benefits, we can calculate the cumulative probability for six or fewer employees and subtract it from one. This approach simplifies the calculation by leveraging previously computed probabilities.
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