Exercice 3 Let X Bin508 Compute PX Solutionn5 P08 Using bino

Exercice 3 Let X -Bin(5,0.8). Compute P(X

Solution

n=5

P=0.8

Using binomial distribution,

P( x <=4) = 0.6723

P( x <=6) = 1

Expectation = np = 4

Variance = np(1 - p) = 0.8

Standard deviation = 0.8944

For the value 4, with continuity correction,

P( x <=4) = p( x <4.5)

Z value for 4.5, z=(4.5-4)/0.8944 =0.56

P( x <4.5) = p( z<0.56) = 0.7123

For the value 6, with continuity correction,

P( x <=6) = p( x <6.5)

Z value for 6.5, z=(6.5-4)/0.8944 =5.03

P( x <6.5) = p( z<5.03) = 1

We are getting same result for the value 6.

But for the value 4, we get the large probability in the normal approximation than binomial.