Suppose 69% of students enrolled at a community college use the college library. A random sample of 31 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 31 students selected: (Report probabilities accurate to at least 4 decimal places.) a) exactly 21 use the college library? l l b) exactly 8 do not use the college library?l l c) all of them use the college library? l l cl) at most 18 use the college library?' l e) at least 15 use the college library?' l f) more than half use the college library?l l g) at least 15 but no more than 24 use the college library? h) less than 13 or more than 23 use the college library? 2. Calculate the mean and standard deviation of students that use the college library. Round to 2 decimal places. Mean : Standard Deviation : 3. If you expect to find exactly 60 students that use the college library, how large a sample should you select? Report the minimum sample size required as an integer