In: Statistics and Probability
Given a binomial random variable with n = 100 and p = .5, estimate the Pr[X ≥ 40]
Solution:
Given that,
P = 0.5
1 - P = 0.5
n = 100
Here, BIN ( n , P ) that is , BIN (100 , 0.5)
then,
n*p = 100*0.5 = 50 > 5
n(1- P) = 100*0.5 = 50 > 5
According to normal approximation binomial,
X Normal
Mean = = n*P = 100*0.5 = 50
Standard deviation = =n*p*(1-p) = 100*0.5*0.5 = 25 = 5
We using countinuity correction factor
P(X a ) = P(X > a - 0.5)
P(x > 39.5) = 1 - P(x < 39.5)
= 1 - P((x - ) / < (39.5 - 50 ) / 5)
= 1 - P(z < -2.1)
= 1 - 0.0179
= 0.9821
Probability = 0.9821