Question

Use the normal approximation to the binomial to find the probability for n=12 p=0.5 and x≥8. Round z-value calculations to 2 decimal places and final answer to 4 decimal places

Answer 1

Solution :

Given that,

p = 0.5

q = 1 - p =1-0.5=0.5

n = 12

Using binomial distribution,

= n * p = 12*0.5=6

= n * p * q = 12*0.5*0.5=1.732

Using continuity correction

,P(x≥8) = 1 - P(x <7.5 )

= 1 - P((x - ) / < (7.5 -6) / 1.732)

= 1 - P(z < 0.87)   

Using z table   

= 1 -0.8078

probability= 0.1922