According to the guideline from the Health Department, every over-weight child needs to take a fitness test. Every ten over-weight children would be randomly grouped together to attend the fitness test. According to the past experience, the probability for each child to pass the fitness test is 0.75 and whether a child can pass the test is independent with the test result of other children. (a) Many test sessions will be conducted regularly, each with 10 independent children. Find the expectation and standard deviation of the number of children can pass the fitness test in a test session.
(b) Most likely, how many children can pass the fitness test in a test session? Justify your answer by comparing the two outcomes with the relatively high probability.
(c) Find the probability that less than 8 children can pass the fitness test in one test session.