Question

In: Statistics and Probability

Given a binomial random variable with n​ = 100 and p​ = .5​, estimate the​ Pr[X...

Given a binomial random variable with n​ = 100 and p​ = .5​, estimate the​ Pr[X ≥ 40​]

Solutions

Expert Solution

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


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