In a large university, 15% of the students are business majors. A random sample of 100 students is selected, and their majors are recorded. (The sample proportion p will be the proportion of business majors in those sampled students.) (a) What are the expected value, standard deviation, and shape of the sampling distribution of p? (8pt.) (b) What is the probability that the sample contains less than 22 business majors? (6pt.) (c) What is the probability that the sample proportion will be within 0.05 of the actual population proportion? (10pt.)