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A probability distribution describes how the probabilities of a random variable are distributed across its possible values. In this context, we can use the binomial distribution since we are dealing with a fixed number of trials (400 employees) and two possible outcomes (believing or not believing that the employer cares). Understanding this distribution is crucial for calculating the probability of fewer than 100 employees expressing concern for their well-being.

The binomial probability formula calculates the likelihood of obtaining a specific number of successes in a fixed number of independent Bernoulli trials. It is expressed as P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success. This formula will help determine the probability of fewer than 100 employees believing their employer cares.

For large sample sizes, the binomial distribution can be approximated by a normal distribution, which simplifies calculations. This approximation is valid when both np and n(1-p) are greater than 5. In this scenario, with 400 employees and a success probability of 0.35, we can use the normal distribution to find the probability of fewer than 100 employees believing their employer cares, making the calculations more manageable.