A study examined national attitudes about antidepressants....

A study examined national attitudes about antidepressants. The study revealed that approximately $70 \%$ believe "antidepressants do not really cure anything, they just cover up the real trouble." According to this study, what is the probability that at least 3 of the next 5 people selected at random will be of this opinion?

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Key Concepts

Bernoulli Trials

Bernoulli trials refer to individual experiments or trials that have exactly two outcomes (commonly labeled as success and failure) and are independent of one another. Each trial has the same probability of success, which is a critical assumption for applying the binomial distribution.

Cumulative Probability

Cumulative probability in the context of the binomial distribution refers to the probability that the number of successes is at least, at most, or exactly a certain value. It is calculated by summing up the probabilities of individual outcomes to give the probability of a range of outcomes, such as 'at least 3 successes in 5 trials', which involves summing the probabilities of 3, 4, and 5 successes.

Binomial Distribution

The binomial distribution is a probability distribution that represents the number of successes in a fixed number of independent trials, each with a constant probability of success. It is used to model events with two possible outcomes—often termed as success and failure—and is characterized by the parameters n (number of trials) and p (probability of success in each trial).

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