Week 2 Homework

Problem 1: The Tiffin Police Department wants you to do further calculations using the annual training for the \(9 \mathrm{~mm}\). Any officer who falls more than one standard deviation below the average must take a remedial shooting course. Any officer who falls one standard deviation above the average will be recommended to take the entry test for the SWAT team. Using the concept of Z-scores, report which officers will be recommended.

Problem 2: The Ohio State Highway Patrol was analyzing quarterly DUI arrests in Northwest Ohio. They determined that if a city had arrests more than 1.5 standard deviations above the regional average that they would assign more patrol cars to the area. If Tiffin had 102 arrests in the last quarter and the regional average was 76.3 with a standard deviation of 13.6, would the highway patrol dispatch more units to Tiffin?

Problem 3: A new academy recruit received back her score from her entrance examination. She was told that her z-score was \(-1.34\) for the written part but her performance in the physical tests had a z-score of \(+2.32\).

1. If the average score on the written part was \(84.5 \%\) and the standard deviation was \(3.6 \%\), what percent did she get on her written exam?
2. If the average score on the physical part was \(75.5 \%\) and the standard deviation was \(6.2 \%\), what score did she get on the physical tests

Problem 4: Two friends were taking a driving course at the police academy. The average completion time of the course was 49.3 seconds, and the standard deviation was 3.7 seconds. If Kathleen finished the course in 54.8 seconds and Scott finished the course in 42.6 seconds, what percent of people could be expected to finish the course with a time in between their two?

Problem 5: In 2000 , the average number of murders per 100,000 people in Ohio's "major" cities was 3.7 with a standard deviation of 0.85. If Toledo averaged 5.1 murders per 100,000 inhabitants, what percentage of major cities had murder rates lower than Toledo?

Problem 6 : Two academy friends who are now detectives, one in San Antonio and one in Cleveland, are conducting simultaneous investigations into drug trafficking arrests made by their respective precincts. Detective A finds the number of arrests made in San Antonio was 42.8 per month. The average number of arrests made in Texas was 35.8 per month with a standard deviation of 5.3. Detective B finds the number of arrests made per month in Cleveland was 38.2. The average number of arrests made in Ohio was 32.6 with a standard deviation of 4.5. Using the concept of standardized scores (z-scores), determine which precinct was "better" in making arrests for drug trafficking compared to their state's average. Explain your conclusion.

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