% of employees judge their peers by the cleanliness of their workspaces. You randomly select 8 employees and ask them whether they judge their peers by the cleanliness of their workspaces. The random variable represents the number of employees who judge their peers by the cleanliness of their workspaces. Construct a binomial distribution using n equals 8 and p equals 0.34.

To construct a binomial distribution for the given problem where \( n = 8 \) (number of trials) and \( p = 0.34 \) (probability of success), we need to calculate the probability of having exactly \( k \) successes out of 8 trials for \( k = 0, 1, 2, \ldots, 8 \).

The probability mass function (PMF) for a binomial distribution is given by:

\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]

where:
- \( \binom{n}{k} \) is the binomial coefficient, calculated as \( \binom{n}{k} = \frac{n!}{k!(n

Learn how to construct a binomial distribution with n=8 and p=0.34. Explore the probability of employees judging their peers based on workspace cleanliness using the binomial probability mass function. Suitable for college-level students studying probability theory.

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