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Unformatted text preview: ls. The possible
values of X are whole numbers that range from 0 to n. As an abbreviation, we say X~B(n, p).
Binomial probabilities are calculated with the following formula: ⎛n⎞ k
P( X = k ) = ⎜
⎟ p (1 − p ) = n Ck p (1 − p )
In R, P( X = k ) = dbinom(k,n, p). With a TI-83/84 calculator, P( X = k ) = binompdf(n, p, k)
Example: A fair coin is flipped 30 times.
What is the probability that the coin comes up heads exactly 12 times? P( X ≤ k ) = pbinom(k,n,p) P( X ≤ k ) = binomcdf(n, p, k) What is the probability the coin comes up heads less than 12 times?
What is the probability the coin comes up heads more than 12 times? The mean and variance of a binomial distribution are computed using the following formulas: µ = E ⎡ X ⎤ = np
⎣⎦ σ 2 = np (1 − p )
17. Suppose it is known that 80% of the people exposed to the flu virus will contract the flu. Out of a family
of five exposed to the virus, what is the probability that:
a. No one will contract the flu?
b. All will contract the flu?
c. Exactly two will get the flu?
d. At least two will get the flu?
e. Let X = number of family members contracting the flu. Create the probability distribution table of X.
f. Find the mean and variance of this distribution....
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This document was uploaded on 02/26/2014 for the course MATH 2311 at University of Houston.
- Spring '08