Chapter 11.3, Problem 2GP

(a)

To determine

To construct: The relative-frequency table of given variable.

Answer to Problem 2GP

The relative frequency table is given below.

Explanation of Solution

Given:

The $X$ variable represents the sum of the values of two spins of the wheel.

  

The minimum sum is $1+1=2$ & the maximum sum is $10+10=20$ for two spins. The total number of possible combinations is $8\times 8=64$ . The table will be

;

Sum	Combination	frequency	Relative frequency
$2$	$1+1$	$1$	$1/64$
$3$	$1+2,2+1$	$2$	$2/64$
$4$	$1+3,2+2,3+1$	$3$	$3/64$
$5$	$1+4,2+3,3+2,4+1$	$4$	$4/64$
$6$	$1+5,2+4,3+3,4+2,5+1$	$5$	$5/64$
$7$	$1+6,2+5,3+4,4+3,5+2,6+1$	$6$	$6/64$
$8$	$2+6,3+5,4+4,5+3,6+2$	$5$	$5/64$
$9$	$1+8,3+6,4+5,5+4,6+3,8+1$	$6$	$6/64$
$10$	$2+8,4+6,5+5,6+4,8+2$	$5$	$5/64$
$11$	$1+10,3+8,5+6,6+5,8+3,10+1$	$6$	$6/64$
$12$	$2+10,4+8,6+6,8+4,10+2$	$5$	$5/64$
$13$	$3+10,5+8,8+5,10+3$	$4$	$4/64$
$14$	$4+10,6+8,8+6,10+4$	$4$	$4/64$
$15$	$5+10,10+5$	$2$	$2/64$
$16$	$6+10,8+8,10+6$	$3$	$3/64$
$18$	$8+10,10+8$	$2$	$2/64$
$20$	$10+10$	$1$	$1/64$

Therefore the relative frequency table is given above.

(b)

To determine

To plot: The graph of the theoretical probability distribution.

Answer to Problem 2GP

The graph is given below.

Explanation of Solution

The horizontal axis would be the sum while the vertical axis is the probability(in decimals).

  

Therefore the graph is given above.