Nina is shopping for a new battery for her laptop computer. She wants the battery to be good enough that it lasts from when she leaves her home in the morning for school until when she arrives back home from school. She often uses her laptop when traveling to and from school. . Brand X has a battery life that is normally distributed with a mean of 9.75 hours and a standard deviation of 1.8 hours. . Brand Y has a battery life that is normally distributed with a mean of 9.5 hours and a standard deviation of 1.1 hours. Would you suggest that Nina purchase a Brand X or Brand Y battery? Use mathematics to justify your conclusion and explain your reasoning. Part 1. Create a normal curve for Brand X and Brand Y labeled with the mean and standard deviation with the corresponding number of hours (1.5 points). Brand X Brand Y gg gg gg battery life hours) 3 (standard deviation) 5 0 0 0 0 [every Me hours ) 2 3 (standard deviation) 12 16 Part 2. Estimate the number of hours of battery life required for 8, 9, and 10 hours using the z-scores for each battery. Explain the meaning of your findings (1.5 points). a) Find the z-score and provide context for the 8 hours of battery life. Brand X Brand Y Z-score: z-score: How likely is this event to occur? How likely is this event to occur?b) Find the z-score and provide context for the 9 hours of battery life. Brand X Brand Y z-score: z-score: How likely is this event to occur? How likely is this event to occur? c) Find the z-score and provide context for the 10 hours of battery life. Brand X Brand Y z-score: z-score: How likely is this event to occur? How likely is this event to occur?How likely is wild Part 3. Based on your calculations in Parts 1 and 2, provide a recommendation to Nina to purchase a Brand X or Brand Y battery with an explanation that considers all aspects of the context and data (1 point)