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4. The legal limit for intoxication in Texas is 0.08% blood alcohol concentration (BAC) Suppose that a driver was tested with a breathalyzer that is subject to the standard error sigma approx0.011% . Answer the following problems using the normal approximation .

4(a) the breathalyzer reading was 0.085% , what is probability that the driver was not legally

4(b) the police officer wants to be at least 95% sure of DUI before arresting a suspected driver , at least how much BAC should he expect from his breathalyzer ?

4 The legal limit for intoxication in Texas is 008 blood alcohol concentration BAC Suppose that a driver was tested with a breathalyzer that is subject to the s class=

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Answer:

The answer is below

Explanation:

The z score is a score used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{p_s-p}{\sigma_p} \\\\Where\ p_s\ is\ the \ sample\ proportion, p\ is\ the\ population\ proportion\ and\\\sigma_p\ is\ the\ standard\ error.\\\\Given\ that\ \sigma_p=0.011\%,p=0.08\%[/tex]

a)

[tex]For\ p_s=0.085\%\\\\z=\frac{0.085-0.08}{0.011} =0.45[/tex]

From the normal distribution table, P(z > 0.45) = 1 - 0.6736 = 32.64%

b) The z score that corresponds to a probability of 95% is 1.65

Therefore:

[tex]1.65=\frac{p_s-0.08}{0.011} \\\\p_s=0.01815+0.08\\\\p_s=0.098\%[/tex]

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