QMB 3200-XYZ University finds that 25% of its students withdraw

[20 points] XYZ University finds that 25% of its students withdraw without completing the calculus course. Assuming 20 students have registered for the courseClearly state what the random variable in this problem is?What is an appropriate distribution to be used for this problem and why?Compute the expected number of withdrawalsCompute the probability that exactly four will withdrawCompute the probability that more than three will withdrawCompute the probability that two or fewer will withdraw[20 points] The average cost per night of a hotel room in San Francisco is $550 with a standard deviation is $150 based on a sample of 50 hotel room rates.Clearly state what the random variable in this problem is?What is an appropriate distribution to be used for finding the confidence intervals for this problem and why?Construct a 99% confidence interval estimate on the mean of all hotel room rates.What is the 90% confidence interval estimate?What is the 95% confidence interval estimate?[20 points] At Western University the historical mean of scholarship examination score for freshman applications is 1000. Population standard deviation is known to be 200. Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed. A sample of 100 applications provided a mean of 1050.State the hypotheses to test whether the mean examination score for the new freshman applications has changed.What is the 95% confidence interval estimate of the population mean examination score?Use the 95% confidence interval to conduct a hypothesis test. What is your conclusion?Assuming ? = .05, conduct p-value based hypothesis test. What is the conclusion?Assuming ? = .05 conduct a critical-value based hypothesis tests. What is the conclusion?How do the results compare in all the three cases?[20 points] The Safety Council estimates that off-the-job accidents cost businesses almost $500 billion annually in lost productivity. Based on their estimates, companies with hundred employees are expected to have six off-the-job accidents per year.Clearly state what the random variable in this problem is?What is an appropriate distribution to be used for this problem and why?What is the probability of no off-the-job accidents during the next six months?What is the probability of at least four off-the-job accidents during a one-year period?What is the probability that the number of off-the-job accidents is more than two but less than six during a four-month period?What is the probability of at the most three off-the-job accidents during the next eight months?