Hi could you solve the problems 1 through 7 (see attached document) so I can check my answers and see how I solved all the problems and how I go about them. Thanks

1. Consider the following data on the number of books borrowed at a Library on 17 randomly picked days: 390 406 446 420 370 328 410 320 368 392 280 325 382 260421370329 (a) Compute the ve-number summary for this dataset and draw the box plot. Are there any outliers? Explain. (b) Is the distribution symmetric? Explain. (c) Find the sample mean and the sample SD. Are those good measures for summarizing this data? 2. Let the random variable X be the number of accidents happening on GW parkway in a given day with the following probability distribution: _____\" (a) Find the probability that there are at most two accidents in a day. (b) Find the mean and standard deviation of the RV. X. How do you interpret these quantities? (c) Suppose a park ranger collected data on 7 different days (randomly selected). What is the probability exactly 2 out of those 7 days were accident-free. 3. Suppose the mean waiting time at a grocery store checkout line is 300 seconds with a standard deviation of 48 seconds. The distribution is positively skewed. Suppose you are waiting in a line. a) What can you say about the chances that it will take you between 3 minutes and 7 minutes? b) What can you say about the probability that you will be done in 2 minutes? 4. Suppose you are shelving 8 books. 5 of them are STAT books and the remaining 3 are History books. If those books are shelved randomly a) what is the probability that all the STAT books are shelved together as well as all the History books are shelved together? b) What is the probability that the STAT books are shelved together? 5. A study of the behavior of large number of drug offenders after treatment for drug abuse suggests that the likelihood of conviction within a two-year period after treatment may depend on the offender's education. The proportions of total number of cases in these categories are shown below: otal (a) Find the probability that a randomly selected offender has nine or less years of education. (b) Given that the offender is convicted (B), what is the probability that the offender has ten or more years of Education (A)? (c) Are the events A and B independent? Explain your answer. 6. A deck of 52 cards has 12 face cards (King, Queen and Jack are called face cards) and 40 non-face cards. A dealer drew 5 cards randomly without replacement from the pack. (a) What is the probability that she has exactly 3 face cards in her hand? (b) What is the probability that she has exactly 2 face cards but none of them is Jack? (o) How does your answer in part (a) changes if the cards were drawn with replacement? 7. A pharmaceutical company reported that when a person is given a vaccine, the probability that the person will develop immunity to a virus is 0.8. Suppose, 12 people are randomly picked and given the vaccine: (a) Find the expected number and standard deviation of people who will develop immunity. (b) Find the probability that exactly half of them will develop immunity