Question

FIND THE PROBABILITY FROM THE DISTRIBUTION GIVEN AT LEAST 29

Answer 1

I don’t have the distribution or its parameters from your message. Tell me which distribution and the parameters (or paste the probability table) and I’ll compute P(X ≥ 29).

Meanwhile, here are the ways to get P(X ≥ 29) for the common cases and how to compute it:

1) If you have a probability table (discrete distribution)
- Sum the probabilities for all x ≥ 29:
P(X ≥ 29) = Σ_{x=29}^{∞} p(x) (or up to the max x in your table).

2) Binomial (X ~ Bin(n,p))
- Exact: P(X ≥ 29) = 1 − P(X ≤ 28) = 1 − Σ_{k=0}^{28} C(n,k) p^k (1−p)^{n−k}.
- R: 1 - pbinom(28, size=n, prob=p)
- Python (scipy): 1 - binom.cdf(28, n, p)
- Normal approximation (large n): mean=np, sd=√(np(1−p)), use continuity correction:
z = (28.5 − np)/√(np(1−p)), P ≈ 1 − Φ(z).

3) Poisson (X ~ Pois(λ))
- Exact: P(X ≥ 29) = 1 − Σ_{k=0}^{28} e^{−λ} λ^k/k!
- R: 1 - ppois(28, lambda)
- Python (scipy): 1 - poisson.cdf(28, lambda)

4) Normal (continuous)
- If X is normal with mean μ and sd σ:
P(X ≥ 29) = 1 − Φ((29 − μ)/σ).

If you tell me the distribution type and parameters (for example, Bin(n=50,p=0.6) or Pois(λ=20) or give the table), I’ll compute the numeric probability for you.