Chapter 11.9, Problem 43PPSE

Solution

a.

To examine: The graph of $y={}^7{C}_x{(0.5)}^x{(0.5)}^{7-x}$ and describe any symmetry in the graph.

The graph is symmetric around $x=3.5$ .

Given information:

The binomial probability formula: $y={}^7{C}_x{(0.5)}^x{(0.5)}^{7-x}$

  

Explanation:

The graph of $y={}^7{C}_x{(0.5)}^x{(0.5)}^{7-x}$ is shown by using the given command on ti-83 calculator.

  

Press [2nd] and then [Calc] to get the maximum value , which is at $x=3$ and $x=4$ .

The right portion of the distribution is equal to the left portion of the distribution for the axis of symmetry of $x=3.5$ . [lies between 3 and 4]

  

The graph is symmetric around $x=3.5$ .

b.

To verify: The symmetry by displaying values of the function in table form.

One output of the function is associated with two input values. Thus, symmetry is verified.

Explanation:

x	$y={}^7{C}_x{(0.5)}^x{(0.5)}^{7-x}$
0	0.0078125
1	0.0546875
2	0.1640625
3	0.2734375
4	0.2734375
5	0.1640625
6	0.0546875
7	0.0078125

One output of the function is associated with two input values.

c.

To change: The graph to $y={}^7{C}_x{(0.6)}^x{(0.4)}^{7-x}$ and check if it has symmetry.

The graph is left skewed. The graph does not have any symmetry.

Explanation:

Use the command shown in the picture to graph $y={}^7{C}_x{(0.6)}^x{(0.4)}^{7-x}$ .

  

The graph of is shown.

  

The left tail is quite longer than the right tail.

The graph is left skewed.