In many states a motorist is legally drunk or driving under the influence (DUI)
ID: 3125507 • Letter: I
Question
In many states a motorist is legally drunk or driving under the influence (DUI) if his/ her blood alcohol concentration (BAC) is 0.10% or higher. When a suspected DUI offender is pulled over, police often request a sobriety test called a Breathalyzer, in which the suspected offender breathes into a machine that reports BAC. Although the Breathalyzers are remarkably precise, they do exhibit some measurement error. Because of that variability, the possibility exists that a driver's true BAC may be under 0.10% even though the Breathalyzer gives a reading over 0.10%.Explanation / Answer
A)
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]
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B)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.1
u = mean = 0.15
s = standard deviation = 0.004
Thus,
z = (x - u) / s = -12.5
Thus, using a table/technology, the left tailed area of this is
P(z < -12.5 ) = 3.73256E-36 [ALMOST 0] [ANSWER]
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c)
FOR THE PROBABILITY THAT ONE OF THEM GETS A DUI CHARGE:
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.1
u = mean = 0.1
s = standard deviation = 0.004
Thus,
z = (x - u) / s = 0
Thus, using a table/technology, the right tailed area of this is
P(z > 0 ) = 0.5
Hence, the probability that a person will not be guilty is 1 - 0.5 = 0.5.
As
P(at least one guilty) = 1 - P(none guilty)
Then
P(at least one guilty) = 1 - 0.5^9 = 0.998046875 [ANSWER]
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