In many states a motorist is legally drunk if his or her blood alcohol concentra

Question

In many states a motorist is legally drunk if his or her blood alcohol concentration (BAC) is 0.10% or higher. Although breath analyzers used for sobriety tests are remarkably precise, the machines do exhibit a certain amount of measurement error. Experience has shown that repeated breath analyzer measurements taken on the same person produce a distribution of responses that can be described by a normal density function with mu equal to the persons true BAC and sigma equal to 0.004%. Suppose two drivers are stopped by police, one with true BAC of 0.095% and one with true BAC of 0.11%. The police officer offers each driver a choice either take the sobriety test once or take it twice and average the readings. Which option should each driver take? Explain, then support your answers with calculations.

Explanation / Answer

In case of first driver

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.1      
u = mean =    0.095      
          
s = standard deviation =    0.004      
          
Thus,          
          
z = (x - u) / s =    1.25      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.25   ) =    0.105649774 [ANSWER]

In case of second driver,

We first get the z score for the critical value. As z = (x - u) / s, then as

          
x = critical value =    0.1      
u = mean =    0.11
          
s = standard deviation =    0.004      
          
Thus,          
          
z = (x - u) / s =    -2.5      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -2.5 ) =   0.0062 [ANSWER]

So, driver 1 should take 2nd option and driver 2 should take 1st option.

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