Performance metrics for binomial distribution in Singapore H2 math

Performance metrics for binomial distribution in Singapore H2 math

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Frequently Asked Questions

The expected value (mean) of a binomial distribution is given by μ = np, where n is the number of trials and p is the probability of success on each trial.
The variance of a binomial distribution is calculated using the formula σ² = np(1-p), where n is the number of trials and p is the probability of success.
The standard deviation (σ) is the square root of the variance and measures the spread or dispersion of the distribution around the mean. A larger standard deviation indicates greater variability.
The binomial distribution can be applied to scenarios involving a fixed number of independent trials, each with two possible outcomes (success or failure), such as coin flips, exam pass/fail rates, or product defect rates.
The PMF gives the probability of obtaining exactly k successes in n trials and is defined as P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) is the binomial coefficient.
Most scientific calculators have built-in functions (like binompdf and binomcdf) to calculate binomial probabilities. Use these functions with the appropriate values for n, p, and k.
The key assumptions are that the trials are independent, the probability of success is constant for each trial, there are only two possible outcomes (success or failure), and the number of trials is fixed.
The CDF gives the probability of obtaining k or fewer successes in n trials, i.e., P(X ≤ k). It represents the sum of probabilities from 0 to k successes.
Binomial distribution is discrete and deals with the number of successes in a fixed number of trials, while normal distribution is continuous and often used to approximate the binomial distribution when the number of trials is large (n > 30).
A binomial distribution can be approximated by a normal distribution if both np > 5 and n(1-p) > 5. This ensures that the distribution is reasonably symmetric.