MA 117 Probability and Statistics Math - Block 4 - 2001

Reading in preparation for Wednesday, Day Three:
  
Chapter Five  
Read about the normal curve and converting to/from standard units pp.78 - 82. 1.   In what year was the normal curve discovered and first put to use?

2.   Some facts about the normal curve (don’t memorize the formula with e, but you should know the following facts):

a) What is the total area under the curve?

b) The standard normal curve is centered at ________

c) The area between -1 and 1 is about _____________________

d) The area between -1 and 0 is about __________________ (hint: use the symmetry of the curve to answer this!)

e) Does the normal curve ever touch the horizontal axis?

3.  Given a mean and standard deviation of some data set, we can convert values to standard units by counting the number of SD’s that value is above/below the mean. Read example 1 about the HANES study.

A) For this set of data, Mean = ___________ and SD = __________. 

61 inches in standard units is a negative number: What is that negative number?

B) What value is -2 in standard units?

C) What is the value 63.5 in standard units?

 

4. In what sense can the normal curve be considered an ideal histogram (as intended by its discoverer), and how can the normal curve represent the distribution of data among a population if it is always centered at 0? (Consider figure 2).

5. Are all data sets well represented by the normal curve? Think of an example of a histogram which we used in class that is not similar in shape to the normal curve.

6. In figure 2, p.81, two histograms are superimposed. Which one represents the true heights of the women, and which represents an approximation to the heights of the women?

 

 

Read pp. 82 to 85 about finding areas under the normal curve. You will need to refer to the normal curve area table on p. A105. Note: For each example, you should do a reality check by eyeballing the shaded area to see if you believe the numerical value you find.

7. Read example 1 (answer is 77%). Can you find the area between -1.4 and 1.4 under the normal curve by using the table? (Sketch a small diagram as well.)

8. Read example 2. Can you find the area between 0 and 1.4 under the normal curve?

9. Read example 4. Can you find the area between -1 and 1.4 under the normal curve?

10. Read example 5. Can you find the area to the right of 1.4 under the normal curve?

11. Read example 7. Can you find the area between 1.2 and 1.4 under the normal curve?

 
Read about percentiles, pp. 88 - 89, 90 - 91. The nth percentile measures the value which marks the data value below which n% of the population lies.

13. The median is the data value below which _________ percent of the data lies. That means that the median is also the ____________th percentile.

14. Is the 5th percentile or the 95th percentile a larger number?

15. Fill in the blanks in this table by guestimating from the graph of family incomes in 1973 (fig. 1 p. 32)

1st percentile

10th percentile

25th percentile

75th percentile

90th percentile
         

16. Read example 10, and try to find the 90th percentile using the same SD and mean for SAT scores. For this example you can use the normal table again.

 
Chapter Six   
Read pp. 97 - 104

1. How often does the National Bureau of Standards weigh NB 10?

2. In table 1, p.99, what is the actual weight in micrograms corresponding to the first entry 409?

3. Based on the first 5 entries in table 1, what would you report the true weight of NB 10 to be?

4. What is the difference between throwing out outliers and fudging your data? Or is there any difference?

5. What is the difference between bias and chance error? Can they ever be the same thing? Can you have one without the other?

6. If biases and chance errors are so prevalent, is there any point in taking exact measurements in the first place?

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