Question

You want to find out whether caffeine mitigates the effect of alcohol on reaction time. To study this, you administer to your subjects a drink that is equivalent to three 12-ounce beers, followed by the equivalent of two cups of coffee. Then your subjects complete a simulated driving task in which they must follow a fixed speed limit while driving on a straight road. Wind periodically and randomly pushes the simulated vehicle right, left, or not at all. Speed is measured in miles per hour above or below the 60-mph speed limit, with 1 mph being the smallest unit on the scale. Suppose the first subject scores 9 mph. Determine the real limits of 9. When measuring weight on a scale that is accurate to the nearest 0.2 pound, what are the real limits for the weight of 120 pounds? When measuring weight on a scale that is accurate to the nearest 0.5 pound, what are the real/limits for the we.ght of 187 pounds?

Answer 1

First Question

lower limit of 9 mph
`j =  8.5 \  mph`

upper limit of 9 mph
`q =  9.5 \  mph`

Second Question

lower limit of 120 pounds is
`i =  119.9 \  pounds`

upper limit of 120 pounds is
`l =  120.1 \  pounds`

Third Question

lower limit of 187 pounds is
`a =  186.75 \  pounds`

upper limit of 187 pounds is
`b =  187.25 \  pounds`

Explanation:

From the question we are told that

The amount of beer administered is three 12-ounce beers

The amount of coffee administered is two cups of coffee

The speed limit is 60-mph

The smallest unit of scale is 1 mph

The first subject scores 9 mph

Generally given that the smallest unit of scale is 1 mph then the deviation of 9 mph will be by
`(1)/(2) \ mph`

Hence the lower limit of 9 mph is

`j =  9 - 0.5`

`j =  8.5 \  mph`

And the upper limit of 9 mph is

`q =  9 + 0.5`

`q =  9.5 \  mph`

Generally given that the measuring weight on a scale that is accurate to the nearest 0.2 pound then 120 pounds will deviate by
`(1)/(0.2) \ pounds`

Hence the lower limit of 120 pounds is

`i =  120 - 0.1`

`i =  119.9 \  pounds`

And the upper limit of 120 pounds is

`l =  120 + 0.1`

`l =  120.1 \  pounds`

Generally given that the measuring weight on a scale that is accurate to the nearest 0.5 pound then 187 pounds will deviate by
`(1)/(0.5) \ pounds = 0.25 \ pounds`

Hence the lower limit of 120 pounds is

`a =  187 - 0.25`

`a =  186.75 \  pounds`

And the upper limit of 120 pounds is

`b =  187 + 0.25`

`b =  187.25 \  pounds`