Problem #1: Reaction Time Research has demonstrated that a pilot's reaction time deteriorates as time increases...

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Problem #1: Reaction Time Research has demonstrated that a pilot's reaction time deteriorates as time increases since their most recent rest period. Suppose that at 10 hours since the pilot's last rest period, reaction time averages 1.8 seconds and is normally distributed with standard deviation of 0.3 seconds. With every additional hour since the pilot's most recent rest period, reaction time increases by 0.25 seconds. The regulatory authority has demanded that reaction time not exceed 3.5 seconds, 98% of the time. a) How long can this pilot safely operate the aircraft (given the stipulations of the regulatory authority) before they require another rest period. minutes b) The air force has experimented with stimulants that reduce the rate of deterioration to 0.15 seconds for every hour beyond 10 since the most recent rest period. What is the probability that a long-range bomber pilot is able to complete a 20-hour mission and maintain a reaction time of three seconds? % c) Instead of asking pilots to use stimulants, one alternative is to invest into training using simulators. This has been demonstrated to improve performance in reaction tests. While it doesn't improve the deterioration of reaction time since the most recent rest period, it does improve the consistency of reaction time. Instead of a standard deviation of 0.3 seconds, the standard deviation is reduced to 0.15 seconds. Using this approach, what is the probability of the long-range bomber pilot completing a 20-hour mission while maintaining a reaction time of three seconds or less? % Problem #1: Reaction Time Research has demonstrated that a pilot's reaction time deteriorates as time increases since their most recent rest period. Suppose that at 10 hours since the pilot's last rest period, reaction time averages 1.8 seconds and is normally distributed with standard deviation of 0.3 seconds. With every additional hour since the pilot's most recent rest period, reaction time increases by 0.25 seconds. The regulatory authority has demanded that reaction time not exceed 3.5 seconds, 98% of the time. a) How long can this pilot safely operate the aircraft (given the stipulations of the regulatory authority) before they require another rest period. minutes b) The air force has experimented with stimulants that reduce the rate of deterioration to 0.15 seconds for every hour beyond 10 since the most recent rest period. What is the probability that a long-range bomber pilot is able to complete a 20-hour mission and maintain a reaction time of three seconds? % c) Instead of asking pilots to use stimulants, one alternative is to invest into training using simulators. This has been demonstrated to improve performance in reaction tests. While it doesn't improve the deterioration of reaction time since the most recent rest period, it does improve the consistency of reaction time. Instead of a standard deviation of 0.3 seconds, the standard deviation is reduced to 0.15 seconds. Using this approach, what is the probability of the long-range bomber pilot completing a 20-hour mission while maintaining a reaction time of three seconds or less? %