(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.