2. Approximately 60% of students from Fundamentals of Statistics do their homework on time. Each student does homework independently. In a group of randomly selected 10 students, what is the probability that at least 3 students will do their homework on time (Event A)? calculate the probability of a complement event for A. [10 marks] 3. According to a recent survey of $1 students at WIUT their average lunch expense at the University Cafeteria costs 13,800 soums with sample standard deviation of 3,300 soums. The management team of the cafeteria claims that average cost of the lunch for the students costs less than 15,000 soums. A level 4 student wants to find out whether the claim made by the management of the Cafeteria is based on statistical evidence. [15 marks] a. Conduct a hypothesis testing to see whether the claim by the management is accurate. Provide all steps along with practical conclusion. Use significance level of 8%. b. Construct a 92% confidence interval for average lunch expenses. 4. Let's assume that employees' salaries at UzAuto Motors are uniformly distributed between $400 and $2,000 per month. The salaries of employees in managerial positions are uniformly distributed between $1,000 and $2,000 per month. [15 marks] a. Find the probability that a randomly selected employee earns more $900. b. Find the probability that a randomly selected employee earns more than $1,300 given that the employee works in a managerial position. c. Find the 78" percentile for the salary of a manager at UzAuto Motors. 5. For the past 35 years, average annual stock return on General Electric Company has been at 6% with a standard deviation of 3.5% Average annual return on market index S&P500 has been 5% with a standard deviation of 3.2% for the same period. A financial manager at General Electric Company claims that the stock of his company has outperformed the market index for the past 100 years. Test the financial manager's claim using the sample data of past 35 years. Keep significance level at 7%. [20 marks] a. State the hypotheses and test statistic. b. Provide your rejection rule, decision and practical conclusions