You are expected to demonstrate critical thinking and your understanding of the content . Answer the following questions and explain your answer.
(1) Mimi made a random guess at 10 true-or-false questions. Let x be the number of correct answers she got. We know that x follows a binomial distribution. Could you identify n (number of trials), p (probability of success) and q (probability of failure) for this binomial distribution? In addition, what is the expected value (μ) and standard deviation (σ), respectively?
(2) Based on the normal distribution table, we get P(z < -2.2) = 0.0139, and P(z > -2.2) = 0.9861. What did you observe from these two probabilities? Why did this happen?
(3) How do you find the 75th percentile of the standard normal distribution ? Please explain your steps.
(4) The weekly STAT 200 study times for all STAT 200 students in UMUC are normally distributed with μ = 18 hours and σ = 6 hours. If 36 STAT 200 students are randomly selected, find the probability that thier mean study time is greater than 20 hours.
(5) Based on the normal distribution table, we get P(z < -2.2) = 0.0139. Without using any other resources, we know immeidately that P(z > 2.2) = 0.0139. What did you observe from these two probabilities? Why did this happen?