Chapter 11.3, Problem 13PPS

(a)

To determine

To find: The graph for the theoretical probability distribution.

Answer to Problem 13PPS

The graph for the theoretical probability distribution is shown in figure 1.

Explanation of Solution

Given;

There is 1 prize for $20, 5 prizes for $10 and 10 prizes for $5.

Calculation:

From the given data, the plot for the theoretical probability distribution is drawn as,

  

Figure 1

In the above graph, the prizes are represented in the x axis while the probability is represented in y-axis.

Thus, the graph for the theoretical probability distribution is shown in figure 1.

(b)

To determine

To find: The expected value.

Answer to Problem 13PPS

The expected value is $1.20.

Explanation of Solution

Given;

There is 1 prize for $20, 5 prizes for $10 and 10 prizes for $5.

Calculation:

The expected value is calculated as,

  $\begin{array}{c}\sum \left[X.P\left(X\right)\right]=0\left(0.84\right)+20\left(0.01\right)+10\left(0.05\right)+5\left(0.10\right)\\ =0+0.2+0.5+0.5\\ =1.2\end{array}$

Thus, the expected value is $1.20.

(c)

To determine

To find: The interpretation and conclusion.

Answer to Problem 13PPS

The interpretation and conclusion are discussed.

Explanation of Solution

Given;

There is 1 prize for $20, 5 prizes for $10 and 10 prizes for $5.

Calculation:

From the part (b), the value of the expected value is positive. As the chance to win a $0.20 for the cost of $1 is there. Thus, the person wants to participate in the raffle,

Thus, the interpretation and conclusion are discussed.