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Binomial probability refers to the likelihood of obtaining a fixed number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. It is calculated using the binomial formula, which incorporates the number of trials, the number of successes, and the probability of success. In this context, P(x ≥ 110) represents the probability of achieving 110 or more successes.

The normal distribution is a continuous probability distribution characterized by its bell-shaped curve, defined by its mean and standard deviation. It is often used to approximate the binomial distribution when the number of trials is large, due to the Central Limit Theorem. This approximation allows for easier calculations of probabilities, especially when dealing with large sample sizes.

Continuity correction is a technique used when approximating a discrete probability distribution, like the binomial, with a continuous distribution, such as the normal distribution. It involves adjusting the discrete value by 0.5 to account for the fact that the normal distribution is continuous. For example, to find P(x ≥ 110) in a normal approximation, one would calculate P(x > 109.5) to ensure a more accurate representation of the binomial probability.