Assume that the manufacturer of Sensor 1 has lots of data from years of testing that indicate that the standard deviation of distance measurements at a pre-defined 5.0 ft distance is 0.1 ft. With 90% confidence, what is the total width (upper limit minus lower limit) of the associated confidence interval (in ft)?

Scenario

Your company makes wheel chairs for people with limited use of their limbs. Because of the limitations, the wheel chair users need to rely on various automated control systems for operation of the chairs. Because of this, there are many safety features that need to be included on the chairs. One of those features are systems to automatically cut power to the chair when moving forward or backward if the chair gets too close to an object. This is typically accomplished by the use of various sensors on the chair.

The new version of your company's chair is looking at adding new sensors for distance recognition (how far the chair is from an object either in front or back of the chair). The engineering manager has asked you to review and test two new sensors to determine their effectiveness and to recommend the use of one of them on your new chairs. You conducted various tests, including one to determine if the sensors could accurately detect objects of different material and surface type at a fixed distance of 5.00 ft from the sensor.

Effective Range Precision

Sensor 1: 0.5 - 25.0 ft 0.1 ft

Sensor 2: 0.25 - 30.00 ft 0.01 ft

Table 1:Test for Recognition of Fixed Distance at 5.00 ft

	Distance Recorded with Sensor (ft)
Object Surface	Sensor 1	Sensor 2
Shiny metal	5.2	5.06
Brick	5.1	5.06
Glass	5.1	5.07
Drywall (painted black)	4.9	5.01
Drywall (painted red)	5.0	4.95
Drywall (painted white)	4.8	5.04
Wood	5.2	5.00
Concrete	5.1	4.96
Vegetation (bushes/grass, etc.)	5.0	5.14