Police departments use exams as part of their promotion process and officers have to score higher than 80% of those taking the t
1 answer:
Answer:
z score for officer1 is 1, he will be promoted.
z score for officer2 is 0.33, she will not be promoted.
Step-by-step 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:
=1
2) z-score of O2 is
=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
You might be interested in
Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.
For the annually rate we have that:
Where
= initial investment.
= annually interest rate in decimal form.
And the exponent (1) represents the full year.
For the quarterly interest rate we have that:
Where
= initial investment.
= quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.
Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
Notice that we are not using the initial investment
since they are the same.
The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
![\sqrt[4]{1.07} =1+ i_{q}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B1.07%7D%20%3D1%2B%20i_%7Bq%7D%20)
![i_{q} = \sqrt[4]{1.07} -1](https://tex.z-dn.net/?f=%20i_%7Bq%7D%20%3D%20%5Csqrt%5B4%5D%7B1.07%7D%20-1)
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.
For the annually rate we have that:
Where
And the exponent (1) represents the full year.
For the quarterly interest rate we have that:
Where
And the exponent (4) the 4 quarters in the full year.
Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
Notice that we are not using the initial investment
The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.
Answer:
Step-by-step explanation:
