Problem 1. A group of graduating seniors is planning to attend graduate school so they took the GRE exam. Each senior is curious to find out what percentage of students score above them on the exam (mean = 500, standard deviation = 100).
y = 475, y = 450, y = 350, y = 600, y = 674, y = 345, y = 625
------------------------------------------------------------------
Problem 1. Answers
Problem 1 asks the question: What is the percentage that out scores the given raw score? (to do that you convert raw scores to Z-scores and find the percentage above)
Raw 475.00 Raw 450.00 Raw 350.00 Raw 600.00
Z -0.25 Z -0.50 Z -1.50 Z 1.00
59.87% 69.15% 93.32% 15.87%
Raw 674.00 Raw 345.00 Raw 625.00
Z 1.74 Z -1.55 Z 1.25
4 .09% 93.94% 10.56%
----------------------------------------------------------------------------------------------
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.
a. What percentage of persons score over 50?
b. What are the chances (%) of finding a politician who scores over 90?
----------------------------------------------------------------------------------------------
Problem 2. Answers
a. What percentage of persons score over 50? Answer: 33%
b. What are the chances (%) of scoring over 90? Answer: Less than 1% (.38%)
----------------------------------------------------------------------------------------------
Problems 3. Army personnel are expected to conform to established weight and fitness standards. In order to qualify for points toward promotion, an officer must not be over or under 1.96 standard deviations from the overall mean weight of 200 lbs. The standard deviation is 35 lbs. Please answer the following questions:
14. What are the chances (%) of finding a soldier that weighs over 270 lbs.?
a. 270.0% b. 50.00% c. 97.72%0 d. 2.28%
------------------------------------------------------------------------------------
Problems 3. Answers
14. What are the chances (%) of finding a soldier that weighs over 270 lbs.? 2.28%
----------------------------------------------------------------------
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:
a. What is the percentage of jails in the state that are over 3200 square feet.
a. 13% b. 38% c. 97% d. 59%
b. What is the percentage of jails in the state that are over 13000 square feet?
a. 13% b. 38% c. 2% d. 59%
------------------------------------------------------------------------------------
Answers Problem 4.
a. 97%
b. 2.28%
----------------------------------------------------------------------------------------------
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. What are the chances (%) of finding an inmate that scores over 210?
a. 29.87% b. 34.46% c. 42.13% d. 60.13%
----------------------------------------------------------------------------------------------
Problem 5. Answer
What are the chances (%) of finding an inmate that scores over 210? 34.46%
---------------------------------------------------------------------
Problem 6. For each of the problems below, convert the requested scores, draw the normal curve, place the mean in the center, and locate the approximate Z-Score location relative to the mean. Compute either the percentile rank, the percentage above, the percentage between, or the requested raw score.
What is the percentage above a raw score of 50 when = 66 and s = 8?
---------------------------------------------------------------------
Problem 6. Answer
1. 97.72%