Problems: Calculating binomial and hypergeometric probabilities

G. Fowler (gof@usna.navy.mil), February 25, 1996.

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Binomial distribution

X has a binomial distribution with 23 trials and probability of a success 0.43. Check each of the following.

1. P(X<=15)=0.99079.
2. P(5<X<=10)=0.57547.
3. P(7<=X<12)=0.92348.
4. P(7<X<11)=0.44757.
5. P(3<X<=15)=0.98855.
6. P(7<=X<=14)=0.89911.
7. P(X=10)=0.16577.

Hypergeometric distribution

W is the number of good objects selected when 10 objects are selected at random and without replacement from G=20 good objects, B=5 bad objects, and so N=G+B=25 total objects.

1. P(W=8)= 0.385375.
2. P(W=3)=0.

Negative Binomial Distribution

Poisson Distribution