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course MTH 152
If your solution to stated problem does not match the given solution, you should self-critique per instructions at
http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.
Your solution, attempt at solution.
If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.
017. normal-curve models
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Question: `q001. Note that there are 8 questions in this assignment.
Sketch a histogram, i.e. a bar graph, showing the distribution of the number of ways to get 0, 1, 2, 3, 4 and 5 'heads' on a flip of 5 coins. Your histogram should show a bar for 0, 1, 2, 3, 4 and 5 'heads', and the height of a bar should represent the number of ways of getting that number of 'heads'.
Sketch also a histogram showing the probabilities of the different outcomes.
Describe both of your histograms.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
- My histogram showed the y-axis representing “# of Ways Per Value” and x axis represented the number of heads out of 5 flips (0, 1, 2, 3, 4, 5 )
- I arranged the bars to ascend vertically as a graph of x = 1,
- The bar denoting the probability of getting 0 heads is level with the ‘1’ ways per value
- Bar of 1 goes to 5.
- Bar of 2 goes to 10
- Bar of 3 goes to 10
- Bar of 4 goes to 5
- Bar of 5 goes to 1
The second histogram was nearly identical to the first, except for the designation of the y axis, being 1/32 - 10/32 (2/16).
0 = 1/32)
1 = 5/32
2 = 10/32 (2/16)
3 = 10/32 (2/16)
4 = 5/32
5 = 1/32
confidence rating #$&*:
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Given Solution: Your first histogram should show 6 bars, one for each of the possible outcomes 0, 1, 2, 3, 4, 5. These bars should sit on top of a horizontal axis, like the x axis, and each should be labeled just below that axis with the outcome (0, 1, 2, 3, 4 and 5).
The heights of the bars will be 1, 5, 10, 10, 5 and 1, representing the numbers of possible ways for the six different outcomes to occur.
Your second histogram should have the same description as the first, except that the heights of the bars will be 1/32 = .0325, 5/32 = .1625, 10/32 = .325, 10/32 = .325, 5/32 = .1625 and 1/32 = .0325.
The vertical scales of the two histograms may of course be different, and both histograms may even look identical except for the labeling of the vertical axis.
Note that the bar representing, say, 2 will extend along the x axis from x = 1.5 to x = 2.5.
Note also that the distribution is symmetric about the central x value x = 2.5, which occurs on the boundary between the x = 2 and x = 3 bars of the graph. That is, the distribution to the left of x = 2.5 is a mirror image of the distribution to the right of x = 2.5.
Self-critique: Good to go. Graphs and geometry is where my strong suit lies, I believe.
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Self-critique rating: