QUESTION 21 2 points SaveAr Part B: uestion 1 Company XYZ manufactures smart watches. Based on a large volume of historical data, the company has determined that the lifespan of a smart watch they manufacture follows the Normal distribution with a mean of 2 years and a standard deviation of 0.5 year. (a) The company would like to provide a warranty of 1 year on their smart watches. What is the probability that a randomly selected smart watch dies (i.e., stops working) before the warranty expires? (2 marks) QUESTION 22 (b) What is the probability that a randomly selected smart watch has a lifespan between 1 year and 3 years? (4 marks) QUESTION 23 4 points Save Answ (c) The company has recently conducted a small-scale study and interviewed 35 loyal customers. The loyal customers were asked about the lifespan of their previously purchased smart watch. Assuming there has been no change to the durability of the company's smart watches (i.e., there has been no change to the lifespan of the smart watches), what is the distribution of the average lifespan of the smart watches from this study? What is the mean of this distribution? What is the standard deviation of this distribution? (4 marks) QUESTION 24 2 points Save Answer Part B: Question 2 A researcher believes that coffee can improve people's performance in memory tests. Six people were invited to complete a memory test before drinking coffee. After the first test, they were given a cup of coffee. One hour later, they were asked to do another memory test. The test scores (out of 100) before and after drinking coffee for each of the participants are presented below: Participant 1 Participant 2 Participant 3 Participant 4 Participant 5 Participant 6 Before Coffee 80 75 65 81 77 86 After Coffee 90 80 70 73 85 84 (a) State the null and alternative hypotheses. (2 marks)QUESTION 25 (b) What distribution does the test statistic follow? What is the value of the test statistic? (4 marks) \fQUESTION 2 points Save Answer Part B: Question 3 You work for a charity. From your organization's donor profiles, you have developed a regression model to predict donations using gender and income. The following is the output from Excel: A B C D E F G H 1 SUMMARY OUTPUT N W Regression Statistics 4 Multiple R 0.834520754 5 R Square 0.696424889 6 Adjusted R Square 0.664469614 7 Standard Error 5.783464159 8 Observations 22 9 10 ANOVA 11 df SS MS F Significance F 12 Regression 2 1457.93385 728.9669 21.79374 1.2065E-05 13 Residual 19 635.5206959 33.44846 14 Total 21 2093.454545 15 16 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 17 Intercept 27.25501501 13.43025369 2.029375 0.056665 -0.854829018 55.36485903 -0.854829018 55.36485903 18 female 9.013811405 3.673859498 2.453499 0.023972 1.324335104 16.70328771 1.324335104 16.70328771 19 income 0.022444169 0.00891098 2.51871 0.020899 0.003793274 0.041095064 0.003793274 0.041095064 (a) Comment on the significance of gender and income at a = 0.05. (2 marks)\fQUESTION 29 (c) Suppose a new female donor has an income of 1800. What would be the predicted donation using the prediction model? (3 marks)