Statistics The Tiffin Police Department

(1)   The Tiffin Police Department has conducted its annual training for the 9mm. You see the scores for the officers. For the data:
a.   Find the percent made by each officer, round to nearest integer
b.   Using a mean of 94.2 and a standard deviation of 1.8, calculate the corresponding standard scores (i.e. z score, not probability) for each officer’s percent.

Officer   Shots
Made   Shots Taken   Percent Made   Standard Score   Officer   Shots Made   Shots Taken   Percent Made   Standard Score
Glenn   79   85           Taylor   95   102
O’Neal   67   72           James   84   90
McFly   87   95           Tanner   88   95
Hawk   69   74           Ford   80   84
Bench   77   80           Sullivan   78   82
Duncan   72   75           Robinson   90   92
Parker   71   74           Masters   81   87

(2) In 2000, the average number of murders per capita (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 capita, what percentage of “major” cities in Ohio had murder rates lower than Toledo?

(3) 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 her San Antonio precinct 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 arrests. Detective B finds the number of arrests made per month in his Cleveland precinct 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 how you reached your conclusion.

(4) Two “math geeks” who work at your precinct, Mike and Dave, are in an argument. Dave is arguing that if you increase every score in a sample by two, you only change the mean and you do not change the standard deviation. Mikeis arguing that if you increase every score in a sample by two, you change both the mean and the standard deviation. Knowing that you have taken a statistics course at Tiffin, they turn to you to settle the argument. Who is correct? Show mathematical proof.