STA Class
13:10:57
•
To find Binomial Random Variable Probabilities
o
1. Use methods from Ch 3
o
2. Use Binomial Point Probability Distribution
Fig 4.33
n = number of trials
p = prob. Of success
q = prob. Of failure
•
Three Children example
o
Find the probability that none of the 3 children get the disease
Fig 4.34
o
Find the prob. That exactly one of the 3 children get the disease
Fig. 4.35
•
Solving Binomial Probabilities
o
Very small n (14) calculate distribution and probabilities using formula.
o
Binomial tables in back of book can be used for values of n = 5, 6, 7, 8, 9, 10, 15, 20,
and 25 (pages 885 – 888)
o
Use Normal approximation for large n (section 5.5)
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To use Binomial Tables:
o
X is binomial with n = 15 and p = .3
o
Tables give
cumulative probabilities
.
o
Find the probability that x is: Fig 4.36
1. At most 3 (what values?) = .297
2. At least 3 = .873
3. Exactly 3 = .17
4. Less than 3 = .127
5. Exceeds 3 = .703
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STA Class
13:10:57
•
Mean and variance of a binomial random variable
o
µ = µ
p, σ²
=
npq
o
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 Fall '07
 Bagwhandee
 Binomial, Probability, Probability theory, #, 60%, 30%, Alafaya, STA Class

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