The Battery Doctor is a car battery shop known for quick service. The amount of time it takes for battery installation is normally distributed with a mean of 15 minutes and a standard deviation of 3 minutes. a. (3 marks) What is the probability that a randomly selected installation will take less than 17 minutes? b. (3 marks) The Battery Doctor offers a $10 discount to the slowest 5% of their installations. How long must an installation take in order for the discount to apply? c. (4 marks) Nathan has just been awarded employee of the month at the Battery Doctor. Nathan's boss tells him that his last 50 installations were surprisingly fast, and that 98% of all random samples of size 50 have an average installation time that is slower than the average installation time of Nathan's 50 installations. What is the approximate average installation time of Nathan's 50 installations? d. (2 marks) Would you be able to answer the question in part (c) if Nathan's boss had considered samples of size 15 instead of 50? Provide a brief explanation to justify your