Question

Police departments use exams as part of their promotion process and officers have to score higher than 80% of those taking the test to be considered for promotion. Officer #1 receives a raw score of 74 and Officer #2 receives a raw score of 68. The mean of all the exam scores is 65 with a standard deviation of 9. 1) Calculate the z score for Officer #1. Will he be promoted? 2) Calculate the z score for Officer #2. Will she be promoted? Please give the z score for each officer's exam and the result

Answer 1

z score for officer1 is 1, he will be promoted.

z score for officer2 is 0.33, she will not be promoted.

Explanation:

Officer 1 get 74 points. O1=74

Officer 2 get 68 points. O2=68

Mean of the exam is 65 and standart deviation is 9 . M=65 and s=9

1) z-score for O1 can be found using the formula:

`(74-65)/(9)` =1

2) z-score of O2 is

`(68-65)/(9)` =0.33

Promotion is gained if an officer (O), scores higher than 80% of the officers taking the exam. This means they need to be at least in the top 20% of the exam. Therefore we look for the corresponding z score for the P(z)=0.2 which is 0.8416. Since z-score of O1 is bigger that 0.8416, he promotes. Officer2 who got 68 from the exam cannot promote since corresponding z-score is less than 0.8416