Question

Consider the probability that more than 92 out of 146 flights will be on-time. Assume the probability that a given flight will be on-time is 63%. Approximate the probability using the normal distribution. Round your answer to four decimal places.

Answer 1

Solution :

Given that,

Using binomial distribution,

= n * p = 146 * 0.63 = 91.98

= n * p * q = 146 * 0.63 * 0.37 = 5.834

Using continuity correction ,

P(x > 92.5) = 1 - P(x < 92.5)

= 1 - P((x - ) / < (92.5 - 91.98) / 5.834)

= 1 - P(z < 0.09)

= 0.4641