Question

The no-show rate for an airline's reservations is 16% in other words the probability is .16 that the person making a reservation will not take the flight. For the next flight, 42 people have reservations. Use normal approximation to the binomial to approximate the following probabilities.

A. what is the probability that exactly 5 people do not make the flight?

B. What is the probability that between 9 and 12 people, inclusive, do not take the flight?

C. What is the probability that at least one person does not take the flight"

D. What is the probability that at most two people do not take the flight?

Answer 1

Let X denote the number of people that make reservation but do not take the flight. Then

Using Normal approximation, we get

a)

Required probability =

{Due to continuity correction as a result of using Normal approximation
for Binomial distribution}

b)

Required probability =

{Due to continuity correction as a result of using Normal approximation
for Binomial distribution}

c)

Required probability =

{Due to continuity correction as a result of using Normal approximation
for Binomial distribution}

d)

Required probability =

{Due to continuity correction as a result of using Normal approximation
for Binomial distribution}