see attached file.
Final Assignment, M261 Math 261 Nov 29-Dec 8 Due by the noontime on Dec 8, 2021 1.a. (5pts) Write a short narrative (no more than 500 words) about two or three things (concepts, or theorems, or techniques, or anything.) that you learned from this class which you think are interesting. b.(5pts) Choose one problem done in the lecture videos that you think is interesting, write down its solution step by step. 2. (20pts) It is believed that 1.6% of a clinic’s patients have TB. A particular blood test yields a positive result for 97% of patients with TB, but also shows positive for 3% of patients who do not have TB. One patient is chosen at random from the clinic’s patient list and is tested. a. What is the probability that if the test result is positive, the person actually has TB? b. If the test result is positive, doctor orders the patient to take the test again, and the second result is also positive, what is the probability the patient has TB?? 3. (20pts) The baggage weights for passengers using a particular airline are normally distributed with a mean 21 lb and a standard deviation of 5 lb. If the limit on total luggage weight is 2115, what is the probability that the limit will be exceeded for 100 passengers? 4. (25pts) To test the effect of a physical training courses on one’s ability, the number of sit-ups that a person could do in 1 minute, both before and after the course, was recorded. The 17 randomly selected participants scored as shown in the following table. B: 29, 31, 33, 25, 43, 54, 28, 36, 32, 37, 33, 29, 39, 31, 29, 33, 32 A: 31, 33, 30, 27, 46, 53, 32, 39, 37, 30, 35, 35, 43, 29, 30, 35, 50 a. Can you conclude that a significant amount of improvement took place? Use . b. Find a 90% confidence interval for . c. Find such that . 5. (20pts) A test about AIDs was given to 21 MIT students and 25 MCPHS students. The results as follows: MIT: MCPHS: , a. Based on these data, can we say in general MCPHS students have higher score than MIT students? Use %. b. Find 99% confidence interval for the difference between MIT and MCPHS students’ scores. 6. (5pts) 15 MCPHS students volunteered to take part in a new experimental vaccine to prevent -variant of covid-19. The results show that the new vaccine worked for twelve of them and failed for other three. Now, you randomly choose two of these volunteers, if you know the new vaccine failed one of them, what is the chance (or probability) the new vaccine failed the other one as well? α = 0.025 μd k P(μd > k) = 95% x = 71.5, s = 12.6 x = 78.5 s = 10.8 α = 2.5 δ