Question

approximate the following binomial probabilities for this continuous probability distribution
p(x=18,n=50,p=0.3)
p(x>15,n=50,p=0.3)
p(x>12,n=50,p=0.3)
p(12<x<18,n=50,p,=0.3)

Answer 1

From normal approximation of binomial distribution

np > 5 and np(1-p)>5 so that

mean =np = 15

a)

p(x=18,n=50,p=0.3)=0

as x is a continuous distributed

b)

z score at x = 15

x is mean so that z value at x =0

p(x>15,n=50,p=0.3)=0.5

c)

p(x>12,n=50,p=0.3)

Z value at 12

Z = (X - ?) / ?
Z = (12 - 15) / 3.24

Z = -0.92593

From z score table

P(x>12) =P(z> -0.92593) = 0.8228

d)

p(12<x<18,n=50,p,=0.3)

Z value at x =18

Z = (X - ?) / ?
Z = (18 - 15) / 3.24

Z = 0.92593

From z score table

p(12<x<18) = P( -0.92593 < Z < 0.92593) = 0.8228-0.1772= 0.6455