Q4 Homework 

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Problem 1. The Political Science Association believes that the mean level of political support for Latino candidates is 40 points with a standard deviation of 10. Determine the percentile ranks of these seven candidates:

         y = 37,  y = 20,  y = 51,  y = 59, y = 35,  y = 45, y = 40

 Answers: Problem 1 asks the question: What is the Percentile Rank? (to do that, you convert raw scores to Z-scores and find the percentage below) 

 Raw        37.00      Raw        20.00      Raw        51.00      Raw        59.00

Z                -0.30      Z              -2.00      Z               1.10       Z               1.90

PR         38.21%      PR         2.28%       PR         86.43%      PR         97.13%

Raw        35.00         Raw        45.00        Raw        40.00

Z              -0.50          Z                0.50        Z               0.00

PR           30.85%     PR             69.15%    PR           50.00%

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Problem 2.  The “truth in politics” scale (TIP) is an instrument designed to measure the integrity of elected officials. The TIP has a mean of 42 and a standard deviation of 18. The more the candidate has lied, the higher her or his score on the TIP scale.

b. What is the percentile rank of a politician who scores 18.96? 

c. What is the percentile rank of a politician who scores 54?

Answers  Problem 2.  

 b. What is the percentile rank of a politician who scores 18.96? 

                                                        Answer: 10th percentile rank 

 c. What is the percentile rank of a politician who scores 54?

                                                        Answer: 75th percentile rank.   

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Problem 3.   Army personnel are expected to conform to established weight and fitness standards. Mean weight is 200 lbs. The standard deviation is 35 lbs. What is the percentile rank of a soldier who weighs 174.1?

a. What is the percentile rank of a soldier who weighs 174.1?

 Answers Problem 3.  

a. 174.1 =           23rd percentile rank.           

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Problem 4.  A random sample of jails was taken in a statewide survey. Based on a mean jail size of 8,000 square feet (standard deviation of 2500), please answer the following questions: 

 c. What is the percentage of jails in the state that are under 5000 square feet?  

Answers Problem 4.  

 c.   11.51%            

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Problem 5.  Inmates are one of the largest groups of under-educated adults in the nation. The Comprehensive Adult Student Assessment System (CASAS) is a popular adult basic education tool that evaluates life skills (math and reading) of persons enrolled in basic education classes. The mean CASAS score is 200 with a standard deviation of 25.

 a. What is the percentile rank of an inmate who scores 191?  

Answers Problem 5.  

a. What is the percentile rank of an inmate who scores 191?  The 35th percentile rank?

 Problem 6. 

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  What is the percentile rank of a raw score of 90 when  = 100 and s = 15?          

  What is the percentile rank of a score of 420 when  = 500 and s = 100?        

  What is the percentile rank of a score of 59.79 when  = 67 and  s = 7.21?

Answers Problem 7.  

  percentile rank of a raw score of 90 when  = 100 and s = 15?    25.14%          

  percentile rank of a raw score of 420 when  = 500 and s = 100?  21.19th 

  percentile rank of a score of 59.79 when  = 67 and  s = 7.21?   15.87%