Suppose 04%% of college students in Business programs study after midnight. A random sample of 27 college students is selected. Assuming independence, use the binomial formula or software (recommended) to answer the following questions. 1. What is the probability that of the 27 college students selected (Report probabilities accurate to at least 4 decimal places.) at exactly 22 study after midnight? bj exactly 3 do not study after midnight? c] all of them study after midnight? chi at most 23 study after midnight? @) at least 17 study after midnight? more than half study after midnight?ci at least 17 but no more than 25 study after midnight? hi less than 16 or more than 24 study after midnight? 2. Calculate the mean and standard deviation of college students that study after midnight Round to 2 decimal places. Standard Deviation = 3. If you expect to find exactly 132 college students that study after midnight, how large a sample should you select? Report the minimum sample size required as an integer