Penguin Bay is a prison in California. One year ago, the warden started a reward & penalty points system based on the behavior of inmates. A recent analysis showed that the 1000 prisoners had an average score of -4 points with a standard deviation of 4 points. The scores are normally distributed. You have been hired as a statistical consultant and you must answer a few questions about the points system.
1. Fat Butch scored a 6 while his cellmate Slim Jim scored a -8. What percentage
of inmates are doing better than Slim Jim but not as well as Fat Butch?
A. About 30%
B. About 39%
C. About 69%
D. About 84%
E. About 99%
2. Inmates with a Z= -2.00 or lower will be sent to a higher security prison. Express this score in terms of the original points.
A. -16 points
B. -12 points
C. -8 points
D. -4 points
E. -2 points
3. The California Department of Prisons reviewed the scoring system and found it to be too strict. They asked you to adjust the scores using this formula: add 31 to the original score and then double it. For example, Fat Butch's new score is 74 and Slim Jim's is 46. What are the new mean, median, and standard deviation for the inmates' scores now?
A. Mean=70, Median=70, Standard Deviation=70
B. Mean =70, Median=70, Standard Deviation=4
C. Mean =54, Median=54, Standard Deviation=4
D. Mean =54, Median=54, Standard Deviation=8
E. There is not enough information to answer this question.
4. Which is the best description of the median of a data set?
A. It is the difference between the highest value and the lowest value.
B. It estimates the typical variation of points from the mean.
C. It is the place where half the area of a histogram lies to the left of
it and half to the right of it.
D. It is the center of a histogram in the sense of a balancing point
5. A study of hospital records reveals that twice as many male as female patients fall out of their hospital beds. What can we conclude?
A. The review is an experiment and men are clumsier than women.
B. The review is an observational study and men are clumsier than women.
C. The review is an experiment and men may not be clumsier than women. There may be other explanations for falling out of hospital beds.
D. Thereview is an observational study and men may not clumsier than women. There may be other reasons for falling out of hospital beds.
PROBLEMSlike 6 7 and 8 will NOT be on the midterm
9. A psychologist is typing the IQ scores of 50 people into a computer, but accidentally duplicates all of the scores so there are actually 100 now instead of 50. Which of the following statements is correct?
A. This mistake will change the mean but not the standard deviation of the list.
B. This mistake will change the first and third quartiles of the list.
C. This mistake will change the median of the list.
D. A, B, and C are all true.
E. A, B, and C are all false.
10. Calculate the median of this list: 5, -3, -2, 0, 4, 5.
A. -1.00
B. 0.00
C. 0.50
D. 2.00
E. 4.00