Question 1 THE DISK BRAKE CASE National Motors has equipped the ZX-900 with a new disk brake system. We define the stopping distance for a ZX-900 to be the distance (in feet) required to bring the automobile to a complete stop from a speed of 35 mph under normal driving conditions using this new brake system. In addition, we define / to be the mean stopping distance of all ZX-900s. One of the ZX-900's major competitors is advertised to achieve a mean stopping distance of 60 feet. National Motors would like to claim in a new advertising campaign that the ZX-900 achieves a shorter mean stopping distance. Suppose that National Motors randomly selects a sample of 81 ZX-900s. The company records the stopping distance of each automobile and calculates the mean and standard deviation of the sample of 81 stopping distances to be 57.8 ft and 6.02 ft., respectively. a Calculate a 95 percent confidence interval for w. Can National Motors be 95 percent confident that / is less than 60 ft? Explain. b Using the sample of 81 stopping distances as a preliminary sample, find the sample size necessary to make National Motors 95 percent confident that X is within a margin of error of one foot of u.Question 2 THE CIGARETTE ADVERTISEMENT CASE @ ModelAge A random sample of 50 perceived age estimates for a model in a cigarette advertisement showed that the sample mean and sample standard deviation were 26.22 years and 3.1432 years. respectively. 3 Use this sample to calculate a 95 percent condence interval for the population mean age estimate for all viewers of the ad. I: Remembering that the cigarette industry requires that models must appear at least 25 years old, does the condence interval make us 95 percent condent that the population mean perceived age estimate is at least 25? Is the mean perceived age estimate much more than 25? Explain. Question 3 How safe are child car seats? Consumer Reports (May 2005) tested the safety of child car seats in 30 mph crashes. They found \"slim safety margins" for some child car seats. Suppose that Cansmuer Reports simulates the safety of the market-leading child car seat. Their test consists of placing the maximum claimed weight in the car seat and simulating crashes at higher and higher miles per hour until a problem occurs. The following data identify the speed at which a problem with the car seat (such as the strap breaking. seat shell cracked. strap adjuster broke. detached from base. etc.) rst appeared: 31.0. 29.4. 30.4. 28.9. 29.7. 30.1, 32.3, 31.1, 35.4. 29.1. 31.2. 30.2. Using the facts that the sample mean and sample standard deviation are 30.2833 and 1.2862. respectively. nd a 95 percent condence interval for the population mean speed at which a problem with the car seat rst appears. Assume normality. Are we 95 percent condent that this population mean is at least 30 mph? Explain. @ CarSeat