Question

Questions 06, 07 and 08 refer to the same data American Airlines has 120 direct flights on a monthly basis from LAX Airport to Tokyo International Airport.  The past experience from the previous year determine that 30% of its direct flights from LAX to Tokyo International Airport arrive late.  Utilize the normal approximation to the binomial distribution to compute the following questions. Requirement Compute the probability 32 or fewer flights will arrive late Round your answer to three decimals the same as in the first four problems

Answer 1

American airlines has 120 direct flights on a monthly basis from LAX Airport to Tokyo International Airport.

The past experience from the previous year determines that 30% of its direct flights from LAX to Tokyo Airport arrive late.

Now, if X be the number of flights, out of the total 120, that arrive late, then X follows binomial distribution with parameters n=120 and p=0.30.

Now, the value of n is too large, to theoretically use the binomial distribution here.

We note that, n*p=120*0.30, ie. 36.

This is also too large to use the poisson approximation to the binomial distribution.

So, this is the ideal condition to use the Normal approximation to binomial distribution.

We note that

Now, this means that we can say that

X approximately follows normal distribution with mean 36 and standard deviation of 5.0199.

So, Z=(X-36)/5.0199 follows standard normal with mean 0 and standard deviation of 1.

Now, we have to find the probability that 32 or fewer flights would arrive late.

So, basically we have to find

Where, phi is the distribution function of the standard normal variate.

From the standard normal table, this becomes

The answer is

The probability that 32 or fewer flights arrive late is 0.213.