Question

Probability distribution showing the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a?

1) Binomial distribution
2) Normal distribution
3) Poisson distribution
4) Uniform distribution

Answer 1

The correct term for the probability distribution representing the number of successes in a fixed number of independent trials with a constant probability of success is the binomial distribution.

Step-by-step explanation:

The probability distribution that shows the probability of x successes in n trials, where the probability of success does not change from trial to trial, is termed a binomial distribution. A binomial distribution is a discrete random variable (RV) that arises from Bernoulli trials, which have only two possible outcomes: success and failure. The binomial random variable X is defined as the number of successes in n independent trials, with the notation X~B(n,p), where p is the probability of success on one trial, and q is the probability of failure, such that q = 1 - p. The mean of this distribution is calculated using the formula μ = np, and the standard deviation is σ = √npq.