P a g e |1 Assignment 2. Due on Friday June 17, 2016 at 4 pm Date of Submission: Course Number: 03-65-205-91 Course Title: Statistics for the Sciences (Distance Education) Instructor: Dr. Kazi Azad Submitted By: Last Name: First Name: ID #: Address: Do Not Write Anything Below This Line Question # 1 Actual Mark 4 Obtained Mark 2 3 4 5 6 7 8 9 10 11 12 Total 12 4 12 8 4 6 12 12 6 12 8 100 P a g e |2 Instructions to complete the assignment: 1. Do all the problems and do by yourself 2. Print Page 1. Fill in it with your information and use it as the cover page for the assignment (must attach this with the assignment) 3. Assignments can be submitted as hand written or typed in the computer 4. Please write assignments legibly and keep at least a 1 inch margin on the left edge 5. Write your complete address on the cover page as well as on the envelope 6. Please DO NOT forget to staple your assignment pages. Write your last name on top of each page with page number. I will not be responsible for any missing page Note: Keep a copy of your submitted assignment! There is no online submission of the assignment. No email attachment please! Assignments will be submitted by post and must be postmarked no later than 4:00 PM on the deadline date. Post assignments to: Dr. Kazi Azad RE: 65-205-91 Distance Education Department of Mathematics and Statistics University of Windsor 401 Sunset Ave Windsor, Ontario, N9B 3P4, Canada If you wish to personally drop off your assignment at the department, please drop it off at: Lambton Tower, Room 10-109 (Dina Labelle). You should submit your assignment by 4:00pm on the due date. P a g e |3 Problems. 1. A businessman in Windsor, Ontario is preparing an itinerary for a visit to five major cities. Each city will be visited once and only once. The distance travelled and hence the cost of the trip will depend on the order in which he plans his route. How many different itineraries (and trip costs) are possible? (4 marks) 2. Four equally qualified runners, John, Bill, Ed, and Dave, run a 100-metre sprint, and the order of finish is recorded. (12 marks) a. How many simple events are in the sample space? (4 marks) b. If the runners are equally qualified, what probability should you assign to each simple event? (2 marks) c. What is the probability that Dave wins the race? (3 marks) d. What is the probability that Dave wins and John places second? (3 marks) 3. Two city council members are to be selected from a total of five to form a subcommittee to study the city's traffic problems. (4 marks) a. How many different subcommittees are possible? (2 marks) b. If all possible council members have an equal chance of being selected, what is the probability that members Smith and Jones are both selected? (2 marks) 4. On the first day of kindergarten, the teacher randomly selects 1 of his 25 students and records the student's gender, as well as whether or not that student had gone to preschool. (12 marks) a. How would you describe the experiment? (2 marks) b. Construct a tree diagram for this experiment. How many simple events are there? (4 marks) c. The table below shows the distribution of the 25 students according to gender and preschool experience. Use the table to assign probabilities to the simple events in part b. (2 marks) Preschool No preschool Male 8 6 Female 9 2 d. What is the probability that the randomly selected student is male? What is the probability that the student is a female and did not go to preschool? (4 marks) P a g e |4 5. An experiment can result in one or both of events A and B with the probabilities shown in the following table: (8 marks) A Ac B 0.34 0.46 Bc 0.15 0.05 Find the following probabilities: a. ( ) (2 marks) b. P(A|B) (2 marks) c. Are events A and B independent? Mutually exclusive? (4 marks) 6. Hospital records show that 12% of all patients are admitted for surgical treatment, 16% are admitted for obstetrics and 2% receive both obstetrics and surgical treatment. If a new patient is admitted to the hospital, what is the probability that the patient will be admitted either for surgery, obstetrics, or both? (4 marks) 7. A county welfare agency employs 10 welfare workers who interview prospective Supplemental Nutrition Assistance Program (SNAP) recipients. Periodically the supervisor selects, at random, the forms completed by two workers to audit for illegal deductions. Unknown to the supervisor, three of the workers have regularly been giving illegal deductions to applicants. What is the probability that both of the two workers chosen have been giving illegal deductions? (6 marks) 8. A university student frequents one of two coffee houses on campus, choosing Tim Hortons 70% of the time and Starbucks 30% of the time. Regardless of where she goes, she buys a decaffeinated coffee on 60% of her visits. (12 marks) a. The next time she goes into a coffee house on campus, what is the probability that she goes to Tim Hortons and orders a decaffeinated coffee? (4 marks) b. Are the two events in part a independent? Explain. (2 marks) c. If she goes into a coffee house and orders a decaffeinated coffee, what is the probability that she is at Starbucks? (3 marks) d. What is the probability that she goes to Tim Hortons or orders a decaffeinated coffee or both? (3 marks) 9. A random variable X has this probability distribution: (12 marks) x p (x) 0 0.1 1 0.3 2 0.4 3 0.1 4 ? 5 0.05 a. Find p(4). (2 marks) b. Find and . (4 marks) c. Calculate the interval 2. What is the probability that X will fall into this interval? (3 marks) d. If you were to select a very large number of values of X from the population, would most fall into the interval 2? Explain. (3 marks) P a g e |5 10. The number X of people entering the intensive care unit at a particular hospital on any one day has a Poisson probability distribution with mean equal to five people per day. (6 marks) a. What is the probability that the number of people entering the intensive care unit on a particular day is two? Less than or equal to two? (4 marks) b. Is it likely that X will exceed 10? Explain. (2 marks) 11. Suppose in a region in Saskatchewan, among a group of 20 adults with cancer, seven were physically abused during their childhood. A random sample of five adult persons is taken from this group. Assume that sampling occurs without replacement, and the random variable X represents the number of adults abused during their childhood period in the sample. (12 marks) a. Write the formula for (), the probability distribution of X. (2 marks) b. What are the mean and variance of X? (4 marks) c. What proportion of the population of measurements falls into the interval ( 2)? Into the interval ( 3)? Do these results agree with those given by Tchebysheff's Theorem? (4 marks) d. What is the probability that at least one person was abused during childhood? (2 marks) 12. A peony plant with red petals was crossed with another plant having streaky petals. The probability that an offspring from this cross has red flowers is 0.75. Let X is the number of plants with red petals resulting from ten seeds from this cross that were collected and germinated. (8 marks) a. What is the probability distribution of X? Write the formula for (). (2 marks) b. Find ( 9). (3 marks) c. Find ( 1)