5. (12 points) The programmer tests the code until three successive results. Suppose that the success 3 probability is 0.7. r=3 p=07 a. (4 pts) What is the probability that he or she will test the code four times?\fc. (4 pts) What is the probability that the number of tests is at most 4?6. (9 points) In a sample of 123 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 22.6 minutes. a. Find a 98% confidence interval for the mean time.b. Determine the minimum required sample size if you want to be 95% confident that the sample mean is within 2.5 minutes of the population mean.10. (14 pts) The Online Exam from Applied Statistics consists of 6 questions. Statistics show that there is a 75% chance that the student will answer to any one of Exam problems correctly. If the number of attempts for each question is unlimited, find the following probabilitiesa. The student will correctly answer the first question after the 4" attempt\fc. What are the average number and SD of attempts up to when the student answers all the questions correctly