1))) Mimi plans to make a random guess at 10 True or False questions.Answer the following questions:

a.Assume random number x is the number of correct answers Mimi gets.Assume, x follows a binomial distribution.What is n (number of trials), p (probability of success in each trial) and q (probability of failure in each trial)?

b.How many correct answers can she expect to get?(Hint:What is the expected value of the binomial distribution?)(Show work)

2))) Mimi plans to make a random guess at a test containing 10 True or False questions.Answer the following questions:

a.What is the probability that Mimi will pass the test (i.e., get at least 6 correct answers)?

b.To get the answer for part (a), what technology did you use?If an online applet was used, please list the URL.If a calculator or Excel was used, please write out the function.

3))) The commuter trains on the Sliver Line for the Washington Metropolitan Area Transit Authority (WMATA) operate every twenty minutes during late night (9:30 pm to close).Assume the distribution of the waiting time is a uniform distribution.

a.Find the height for this uniform distribution.

b.Find the probability of waiting more than 10 minutes.