In Exercises 9–14, write the binomial probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability.


P(x > 65)

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 on each trial. This concept is essential for understanding scenarios where outcomes are binary, such as success/failure or yes/no.

The normal distribution is a continuous probability distribution characterized by its bell-shaped curve, defined by its mean and standard deviation. It is significant in statistics because many phenomena tend to approximate a normal distribution under certain conditions, particularly when the sample size is large. The normal distribution allows for easier calculations and interpretations of probabilities compared to discrete distributions like the binomial.

Continuity correction is a technique used when approximating a discrete probability distribution, such as the binomial distribution, with a continuous distribution, like the normal distribution. This correction involves adjusting the discrete value by 0.5 units to account for the fact that the normal distribution is continuous. For example, to find P(x > 65) in a binomial context, one would calculate P(x > 65.5) in the normal approximation.