Excel Assignment 3 - The Probability of Continuous Values and Sample Means Probabilities and Scores for Continuous Variables Use this video to complete #1 and #2 in this assignment. 1. Theodore is the owner of FlightPro (an app that provides maps and real-time weather reports for pilots) and is not satisfied with the map download speeds on electronic devices ( = 90 seconds, = 30 seconds, normally distributed). However, he must do a demonstration of the app for a group of investors today (who expect a maximum of 60 second download speeds) and has no time to work on fixing the download speeds. Before giving the demonstration, Theodore wants to predict how likely the following outcomes will be. a. What is the probability that the device he uses in the demonstration will have a download speed of 60 seconds or less or p (X 60)? (1 point) b. What is the probability that the device he uses in the demonstration will have a download speed longer than 60 seconds p (X > 60)? (1 point) c. Which outcome above [p (X 60) or p (X > 60)] is more likely? Explain why you think this is based on the mean/standard deviation of download speeds and what the distribution looks like. (1.5 point) 2. Theodore wants to hire a Software Developer to help him decrease the download speed of FlightPro. His friend is an Instructor at Full Sail University for the Software Development program and has offered to help him find a Software Developer among their graduates from the last year. Over the past year, the cumulative GPA among Software Development graduates at Full Sail University was normally distributed with a mean of = 3.0 with a standard deviation of = 0.5. a. His initial criteria for considering a graduate for hire is having a GPA above 3.75. What proportion of graduates would be considered for hire or p (X > 3.75)? (1.5 point) b. Instead of focusing on a specific GPA, Theodore decides to rely on percentiles to determine the criteria for considering a Software Developer for hire. He decides to consider anyone with a GPA in the 80th percentile for hire. What GPA is at the 80th percentile? (1 point) c. Among all the hiring criteria stated above, which will lead to the largest pool of candidates (GPA > 3.75 or GPA in 80th percentile)? (1.5 point) d. Among all the hiring criteria stated above, which will lead to the highest quality pool of candidates (GPA > 3.75 or GPA in 80th percentile)? (1.5 point) Probabilities and Estimation with Continuous Sample Means Use this video to complete #3 - #5 in this assignment. 3. Theodore is the owner of FlightPro (an app that provides maps and real-time weather reports for pilots) and is not satisfied with the map download speeds on electronic devices ( = 90 seconds, = 30 seconds, normally distributed). So, he hires a Software Developer to reprogram the map feature in FlightPro with the hope that map download speeds will decrease to at least an average of 60 seconds. After the software update, Theodore takes a sample of 3 electronic devices to see how long a map of the Las Vegas airspace takes to download. a. What is the probability that Theodore's sample will have a sample mean of 60 seconds or less (by random chance) even if the software update did not improve download speeds for maps or p ( X 60)? (1.5 point) b. What is the probability that Theodore's sample will NOT have a sample mean of 60 seconds or less (by random chance) even if the software update did not improve download speeds for maps or p ( X > 60)? (1 point) c. If Theodore's sample does have a sample mean of 60 seconds or less after the software update, should he be confident that the software update actually had the desired effect? Explain based on the probabilities above. (1.5 point) 4. Theodore is the owner of FlightPro (an app that provides maps and real-time weather reports for pilots) and is not satisfied with the map download speeds on electronic devices ( = 90 seconds, = 30 seconds, normally distributed). So, he hires a Software Developer to reprogram the map feature in FlightPro with the hope that map download speeds will decrease to at least an average of 60 seconds. After the software update, Theodore takes a sample of 3 electronic devices to see how long a map of the Las Vegas airspace takes to download. Based on a mean download speed from 3 electronic devices being 60 seconds after the software update: a. What is the 90% confidence interval for the average download speed of maps in FlightPro after the update? (1.5 point) b. Explain what this suggests about the new download speed among all devices (be specific and mention the mean download speed before the update). (2 points) 5. Theodore is the owner of FlightPro (an app that provides maps and real-time weather reports for pilots) and is not satisfied with the map download speeds on electronic devices ( = 90 seconds, = 30 seconds, normally distributed). So, he hires a Software Developer to reprogram the map feature in FlightPro with the hope that map download speeds will decrease to at least an average of 60 seconds. After the software update, Theodore takes a sample of 3 electronic devices to see how long a map of the Las Vegas airspace takes to download. Let's say Theodore's mean download speed from 3 electronic devices after the software update was actually 75 seconds. Based on a mean download speed from 3 electronic devices being 75 seconds after the software update: a. What is the 90% confidence interval for the average download speed of maps in FlightPro after the update? (1.5 point) b. Explain what this suggests about the new download speed among all devices (be specific and mention the mean download speed before the update). (2 points)