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Binomial Distribution Mean

μ=np\mu = n p

Worked example: 100 trials at p = 0.3 → mu = 30 — press Try an example to run it live, then adjust anything.

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Binomial Distribution Mean explained

μnp

Expectation is linear, so the average number of successes is simply the per-trial chance repeated n times: μ = np. Toss a fair coin 100 times and expect 50 heads; screen 100 parts with a 3% defect rate and expect 3 defects. Enter p as a decimal from 0 to 1, or switch that input to %.

Reversed, this is the estimator behind opinion polling and quality control: if 25 heads appeared in an experiment with a fair coin, n = 25/0.5 = 50 tosses; if 12 defects turned up in 400 units, p = 12/400 = 0.03. Two traps deserve naming. First, the mean need not be an achievable outcome — 10 rolls of a die average 10/6 ≈ 1.67 sixes, and nobody ever rolls two-thirds of a six. Second, the mean says nothing about spread on its own; pair it with the variance np(1 − p) before deciding whether an observed count is surprising.

Binomial Distribution Mean formula

μ=np\mu = n p
Where
  • μ\mu= Expected number of successes
  • nn= Number of trials
  • pp= Probability of success per trial

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