Instructor: A.E.Cary. Math 243 Final Exam

Transcription

1 Name: Instructor: A.E.Cary Instructions: Show all your work in a manner consistent with that demonstrated in class. Round your answers where appropriate. Use 3 decimal places when rounding answers. The entire exam is closednote, closed-book. You may use your calculator and Excel throughout the entire exam. You may also use the formula sheet provided to you. Wherever you use Excel or your calculator, make sure that any calculations you do are clearly included in your work. 1. The data below shows the length (in minutes) of a sample of 22 movies: (a) Draw a stem-and-leaf plot using a scale such that 8 1 = 81. Use this to construct a frequency histogram. (b) Find the mean, first quartile, median, third quartile, and standard deviation for this data set. State what you use to calculate each of these. Q1: median: Q3: (c) Are there any outliers? Justify your response. (d) Describe the shape of this distribution (e.g. unimodal, bimodal, symmetric, skewed, etc.). (e) Write down your favorite movie. Seriously. I need some suggestions for break. [9 points, 3 points, 2 points, 2 points, 2 extra]

2 2. Out of a class of students, 84% had seen the movie Star Wars, 70% had seen the movie The Hunger Games, and 60% had seen both Star Wars and The Hunger Games. (a) What s the probability that a student has seen either Star Wars or The Hunger Games? (b) Given that a student has seen the movie Star Wars, what s the probability that they have seen The Hunger Games? 3. Out of a group of students, 75% own a smartphone. Of those that own a smartphone, 80% have a Facebook account. Of those that do not own a smartphone, 45% have a Facebook account. (a) Draw a tree diagram representing this scenario. (b) What s the probability that a given student has a Facebook account? [3 points, 6 points; 6 points, 3 points] Instructor: A.E.Cary Page 2 of 6

3 4. An insurance policy will pay policyholders $50,000 if they suffer a major injury. It will pay $10,000 if they suffer a minor injury. Assume that 1 in every 4000 policy holders will suffer a major injury and 1 in every 1000 policy holders will suffer a minor injury (a) Complete the probability model below representing the payout of a given policy. Outcome Payout Probability (b) What s the expected payout for a given policy? 5. A soccer player makes 84% of the penalty kicks that she shoots. (a) If she shoots 10 penalty kicks one season, what s the probability that she makes all 10? (b) If she shoots 10 penalty kicks one season, what s the probability that she makes exactly 7? [8 points; 4 points, 6 points] Instructor: A.E.Cary Page 3 of 6

4 6. A Gallup poll asked 1050 randomly chosen adults if they are familiar with the current VW emissions scandal. Of this sample, 75% said that they were familiar with the scandal. (a) Construct a 95% confidence interval for the proportion of all US adults that are familiar with the VW emissions scandal. (b) Explain what 95% confidence means in this context. 7. It is claimed that 42% of US college grads had a mentor in college. For a sample of college grads in Colorado, it was found that 502 out of 1045 had a mentor in college. You are going to test the claim that the proportion of college grads in Colorado who had a mentor is greater than that of all US college grads. (a) State the null and alternate hypotheses. (b) Calculate the P -value. Round accurately to 5 decimal places. Then decide if you want to reject H 0 or fail to reject H 0 and write a clear summary. [6 points, 2 points; 2 points, 8 points] Instructor: A.E.Cary Page 4 of 6

5 8. Tillamook Cheese makes 2 pound blocks of cheddar cheese. The average block actually has 32.4 ounces with a standard deviation of 0.5 ounces. Assume that this distribution is Normal. (a) What s the probability that a single block contains less than 32 ounces? (b) Out of a sample of 12 blocks, what s the probability that the average weight is less than 32 ounces? [6 points, 6 points] Instructor: A.E.Cary Page 5 of 6

6 9. Table 1 shows the average life expectancy (in years) for a white Table 1 male in a give decade. (We ll use 1 to represent ). Decade Life expectancy (a) Write the least squares regression line that predicts life expectancy. Show all necessary calculations r = r 2 = x = 6.5 ȳ = s x = s y = (b) Calculate the predicted life expectancy for a white male in Table 2 below shows the number of oranges per tree and the average weight (in lbs) of each orange for a sample of orange trees. (a) Use Excel to calculate the following: r = Table 2. Orange Tree Data r 2 = s x = s y = x = ȳ = Num. of Oranges per tree Ave. weight (in lbs) (b) Interpret the value of r 2. [8 points, 2 points; 6 points, 2 points] Instructor: A.E.Cary Page 6 of 6