TASK #2 Math II - FATHOM 10 coin Flips (How many coins would you predict land on heads?)
· Open a new Fathom Workspace.
· Drag a collection, , from the shelf into the workspace.
· Open the collection by positioning the cursor at the lower right hand corner of the collection icon (as shown below). Finally, click and drag when the cursor changes to a resizing icon. Make the collection larger. This will effectively open the collection so that you can see what is inside of it.
· With the open collection selected, choose New Cases… under the Collection menu (as shown at the right). Choose 10 cases and press OK.
· 10 new gold icons should be created in the collection after the last step. Double click on one of the icons to open up the inspector window.
· In the Inspector window under the Tab Cases and the Column Attribute click on the word new and type in the word “Flip”
· Two cells to the right of the cell you just labeled “Flip” double click the space under “Formula”
In the calculator window Type
and press OK. This should cause either an “H” or “T” to appear in the value cell.
· Next, at the top of the Inspect Collection 1 window click on the Display Tab. Then, double click on the cell to the right of caption and under Formula as shown below. When the Formula window opens up click the next to the word Attributes. Double click on the word “Flip”. Finally, press OK.
· The last step should have caused the title underneath each gold ball representing a case to change to either “H” or “T” depending on which the case is representing. Fathom can even take it a step further and have the icon be a picture of a coin Heads up or Tails up depending on the value of the “Flip” for each case.
· This time in the Inspect Collection 1 window and under the formula cell for image double click to open the formula editor. In the formula editor type: . You can select the different Icons by clicking on the next to Icon Names.
· First click on the “Measures” tab in the Inspect Collection window. Click on the text <new> and type in “NumberofHeads”
· Double click on the cell to the right of “NumberofHeads” and under Formula. Then in the formula window type in
and click on OK.
· With the collection highlighted, select Collect Measures from the Collection menu.
· The last step will cause Fathom to re-randomize the 10 coin flips and then record the information from that group in a new collection. Fathom at its default setting will collect 5 sets of coin flips. Open the newly created measures by resizing the measures box created. Double click on one of the green cases inside.
· In the Inspect Measures from Collection window select the Display tab and double click on the Formula cell to the right of caption. This will open the formula window again. Click the next to Attributes and double click the attribute “NumberofHeads”. Finally, click OK .
· The last step will change the title underneath each Measure to the number of Heads flipped in the sample. Currently, we only have 5 sets of 10 coins being flipped. Lets quickly create a 1000 more sets of 10 coin flips. Click on the “Collect Measures” tab in the inspector window.
· First, unselect the “Animations on” and change the number of measures from the default of 5 to as many trials as you would like.
Finally, click on .
· Click on the “Cases” tab in the inspector window and then drag a Graph, , into the workspace.
· Drag the word “NumberofHeads” from the Inspector window onto the x-axis of the graph.
· Click on the arrow to the right of word and change the graph into a histogram as shown at the right.
· The histogram looks fairly normally distributed.
· In order to overlay an actual normal curve on top of the histogram to see how normal the distribution looks, it will be easier if we look at the histogram using a relative frequency rather than just the actual frequency. With the graph selected, under the Graph menu change the Scale to Relative Frequency as shown at the right.
· While the graph is still highlighted, this time select Plot Function from the Graph menu.
· In the formula window type in:
and push OK .
· You can experiment with taking new collections in the measure menu and very consistently demonstrate that this is consistently a very normal distribution.