MATH1P98 - Assignment #2 - Section #1,2 Due: Monday, October 17 @ 11:59 pm Students are expected to complete all questions on the assignment. However, only a subset of questions will be considered for marking. Marks will be deducted for incomplete assignments. Assignment submissions must be neat, legible, written on one side of the page only, and questions must be submitted in order. A cover page must be attached to the front of the assignment (see sample cover page on Sakai). Staple all pages on the top left corner. Please submit answers to the following questions to your assignment drop box by 11:59pm of the due date. The text is Elementary Statistics using Excel (5th Edition), by M. Triola. 1. (Law of Large Numbers, p. 156). Simulate the experiment: rolling of two dice using Excel to find the rolled sum. Follow the instructions: - Open a new Excel document. - Click on cell A1, then click on the function icon fx and select M ath&T rig, then select RAN DBET W EEN . - In the dialog box, enter 1 for bottom and enter 6 for top. - After getting the random number in the first cell, click and hold down the mouse button to drag the lower right corner of this first cell, and pull it down the column until 25 cells are highlighted. When you release the mouse button, all 25 random numbers should be present. - Repeat the steps b) to d) for the second column. - Put the rolled sum of two dice in the third column: Highlight the first two cells in the first row and click on AutoSum icon. Once you receive the sum of two values in the third cell, repeat the step d) to get rolled sum for all 25 values. - Attach the screenshot of your Excel file to your assignment. a) Find the (classical) probability that the rolled sum of two dice is equal to 9. b) Based on the results of experiment (25 trials), estimate the probability (relative frequency approximation) that the rolled sum of two dice is equal to 9. c) Repeat the simulation experiment for 50 and 100 trials, and estimate the probability (relative frequency approximation) that the rolled sum of two dice is equal to 9 for each experiment. Which probability has the closest value to the classical probability? d) Briefly explain how these experiments demonstrate the Law of Large Numbers. 1 e) Construct the (classical) probability distribution of a rolled sum associated with the rolling of the two dice. 2. (Credit Card Purcases, problem 30, p. 167). In a survey, 169 respondents say that they never use a credit card, 1227 say that they use it sometimes, and 2834 say that they use it frequently. a) What is the probability that a randomly selected person uses a credit card frequently? b) Is it unlikely for someone to use a credit card frequently? c) How are all of these results affected by the fact that the responses were obtained by those who decided to respond to the survey posted on the Internet by America Online? 3. The probability that a visit to a primary care physicians (PCP) office results in neither lab work nor referral to a specialist is 35%. Of those coming to a PCPs office, 30% are referred to specialists (event A) and 40% require lab work (event B). a) Draw a Venn diagram and identify the following probabilities: P (A), P (A), P (B), P (B), P (A or B), P (A or B). b) Determine the probability that a visit to a PCPs office results in both lab work and referral to a specialist. c) Determine the probability that a visit to a PCPs office will result in lab work given that he/she has referred to a specialist. 4. A group of 22 students decided to play soccer, and they need to be divided into two teams of 11. Two people can be goalies, 4 people can play as forwards and the rest can play either defense or midfield. a) In how many ways can two forwards be chosen on each team if there are four forwards available? a) In how many ways can 22 students be divided into two equal groups if each team has one goalkeeper and two forwards? 5. There are 20 apples in a basket: 5 Macintosh and 10 Gala and 5 Spartan. You randomly select two apples. a) Develop a tree diagram of all possible outcomes of this experiment. b) Find the probability that the first apple is Gala and the second is Macintosh. c) Find the probability that at least one apple is Spartan. 6. A family has 3 children. a) Construct the probability distribution for x, the number of girls. 2 b) Find the mean and standard deviation for the number of girls. c) Is it a binomial distribution? Why or why not? 7. According to Statistics Canada (Share of Non-Alcoholic Beverage Market, 2008), 16% of Canadians consume coffee, 12% - tea, 72% - others. Twenty five people have registered for a workshop on potential health hazards associated with consumption of caffeine in food and dietary supplements. a) Find the probability that exactly five people from the list of participants prefer drinking either tea or coffee. Calculate the probability manually and check your answer using Excel. b) Find the probability that at least two people out of 25 prefer drinking coffee. Calculate your answer manually and check your answer using Excel. c) What is the average number of people who prefer tea or coffee? 3