Question

Use the normal approximation to find the indicated probability. The sample size is n, the population proportion of successes is p, and X is the number of successes in the sample. n = 81, p = 0.5: P(X ≥ 46)

Answer 1

Solution :

Given that,

p = 0.5

q = 1 - p =1-0.5=0.5

n = 81

Using binomial distribution,

= n * p = 81*0.5=40.5

= n * p * q = 81*0.5*0.5=4.5

Using continuity correction

,P(x >46 ) = 1 - P(x < 45.5)

= 1 - P((x - ) / < (45.5-40.5) / 4.5)

= 1 - P(z < 1.11)   

Using z table   

= 1-0.8665

probability= 0.1335