I need help with the following questions. Please help with the attachment.

1. A bike courier needs to make deliveries at 6 different locations. How many different routes can he take? 2. There are 15 juniors and 20 seniors in the Stat Club. The club is to send four representatives to the Joint Statistical Meetings. If the members of the club decide to send two juniors and two seniors, how many different groupings are possible? 3. Assume random variable x follows a probability distribution shown in the table below. Determine the mean and standard deviation of x. x -2 0 1 2 3 P(x) 0.1 0.1 0.3 0.2 0.3 4. A sample of 10 LED light bulbs consists of 1 defective and 9 good light bulbs. A quality control technician wants to randomly select two of the light bulbs for inspection. Find the probability that the first selected light bulb is good and the second light bulb is also good. A. Assuming the two random selections are made with replacement B. Assuming the two random selections are made without replacement 5. There are 1000 students in a high school. Among the 1000 students, 200 students take AP Statistics, and 250 students take AP French. 100 students take both AP courses. Let S be the event that a randomly selected student takes AP Statistics, and F be the event that a randomly selected student takes AP French a. Provide a written description of the event (S OR F). b. What is the probability of complement event of (S OR F)? 6. Assume the weights of men are normally distributed with a mean of 170 lbs and a standard deviation of 30 lbs. a. Find the 75th percentile for the distribution of men's weights. b. What is the probability that a randomly selected man weighs more than 200 lbs? 7. Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500 and a standard deviation of 100 a. If a random sample of 64 test scores is selected, what is the standard deviation of the sample mean b. What is the probability that 64 randomly selected test scores will have a mean test score that is between 475 and 525 8. A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a 90% confidence interval estimate of the proportion of adults believing in global warming 9. In a study designed to test the effectiveness of garlic for lowering cholesterol, 49 adults were treated with garlic tablets. Cholesterol levels were measured before and after the treatment. The changes in their LDL cholesterol (in mg/dL) have a mean of 3 and standard deviation of 14. Construct a 95% confidence interval estimate of the mean change in LDL cholesterol after the garlic tablet treatment 10