CEG2002] A2. (a) Each sample of water has a 10% chance of containing a particular organic pollutant. Assume that th...
CEG2002] A2. (a) Each sample of water has a 10% chance of containing a particular organic pollutant. Assume that the samples are independent with regard to the presence of the pollutant. Find the probability that in the next 18 samples, exactly 2 contain the pollutant. (b) One of the variables in car crash safety tests is the severity of a driver's head injury when the car is in a head-on collision with a fixed barrier while traveling at 35 miles per hour. The more points assigned to the head injury rating, the more severe the injury. The head injury ratings can be shown to be approximately normally distributed with a mean of 605 points and a standard deviation of 185 points. One of the crash-tested cars is randomly selected from the data and the driver's head injury rating is observed. (i) Find the probability that the rating will fall between 500 and 700 points. (ii) For what rating will only 10% of the crash-tested cars exceed? (c) Suppose that if a measurable amount of rain falls during the next 24 hours, a river will reach loods stage and a business will in- cur damages of 300,000 pounds if a product line is not shutdown, but the damages will be reduced to 3,000 pounds if the product line is shutdown in advance. The product line can make a profit of 20,000 pounds per day when it runs normally. The National Weather Services has indicated that there is a 5% chance of a mea- surable amount of rain during the next 24 hours. needs to decide whether the product line should be shutdown. The manager (i) Draw a decision tree. (ii) Which decision would the manager make based on the mini max criterion? (ii) Which decision would the manager make based on expected- value decisions? mar Turn overl
CEG2002] A2. (a) Each sample of water has a 10% chance of containing a particular organic pollutant. Assume that the samples are independent with regard to the presence of the pollutant. Find the probability that in the next 18 samples, exactly 2 contain the pollutant. (b) One of the variables in car crash safety tests is the severity of a driver's head injury when the car is in a head-on collision with a fixed barrier while traveling at 35 miles per hour. The more points assigned to the head injury rating, the more severe the injury. The head injury ratings can be shown to be approximately normally distributed with a mean of 605 points and a standard deviation of 185 points. One of the crash-tested cars is randomly selected from the data and the driver's head injury rating is observed. (i) Find the probability that the rating will fall between 500 and 700 points. (ii) For what rating will only 10% of the crash-tested cars exceed? (c) Suppose that if a measurable amount of rain falls during the next 24 hours, a river will reach loods stage and a business will in- cur damages of 300,000 pounds if a product line is not shutdown, but the damages will be reduced to 3,000 pounds if the product line is shutdown in advance. The product line can make a profit of 20,000 pounds per day when it runs normally. The National Weather Services has indicated that there is a 5% chance of a mea- surable amount of rain during the next 24 hours. needs to decide whether the product line should be shutdown. The manager (i) Draw a decision tree. (ii) Which decision would the manager make based on the mini max criterion? (ii) Which decision would the manager make based on expected- value decisions? mar Turn overl