A Department of Transportation report about air travel found that, nationwide, 78% of all flights are on time. Suppose a random sample of 50 flights is selected from all nationwide flights that were completed in the past 30 days (over 1000 flights). Let the random variable X be defined as the number of sampled flights that arrived on time. a) How many flights would you expect to be late ? b) Calculate the standard deviation ? c) What is the probability you will have exactly 80 flights on time ? d) What is the probability you will have 20 or less flights that are late ? e) What is the probability you will have more than 100 on time ?