Question

Suppose that a teacher fails p = 35% of his students. Given a class of 200 students. Use the normal approximation to the binomial distribution to estimate the probability that he fails 66 or fewer students.

Answer in book: 0.3015

Just Need work

I know this is the probability for z< -0.52 but can't figure out how to get there

Answer 1

Solution :

Given that,

p = 0.35

q = 1 - p =1-0.35=0.65

n = 200

Using binomial distribution,

Mean = = n * p = 200*0.35=70

Standard deviation = = n * p * q =  200*0.35*0.65=6.7454

Using continuity correction ,

P(x< 66 ) = P((x - ) < (66.5-70) / 6.7454)

= P(z <-0.52 )

Using z table

Probability =0.3015