Note: Round all probabilities to 4 decimal places.

Based on the Bureau of Transportation Statistics, it was reported that the total number of Delta Airlines flights arriving at Seattle/ Tacoma International airport in August of this year was 2579. Out of 2579 flights, 2263 flights arrived on time.

A random sample of 200 flights was randomly chosen, calculate the following probability.

a. Describe whether the condition for a binomial distribution had been met? Explain in the context of the problem.

b. What is the probability a flight will arrive on time.

c. What is the probability exactly 165 flights will arrive on time?

d. What is the probability more than 170 flights will arrive on time.

e. What is the probability at least 180 flights will arrive on time.

f. Calculate the mean and the standard deviation. Interpret the mean Round to one decimal place