Chapter 11.3, Problem 14PPS

(a)

To determine

To find: The expected number of students who will run.

Answer to Problem 14PPS

The expected number of students who will run is 4

Explanation of Solution

The expected value is calculated as,

  $\begin{array}{c}E\left(X\right)=\sum \left[X.P\left(X\right)\right]\\ =\left(X_{1}P\left(X_1\right)+\mathrm{........}+X_{n}P\left(X_n\right)\right)\\ =1\left(0.05\right)+2\left(0.15\right)+3\left(0.1\right)+4\left(0.15\right)+5\left(0.35\right)+6\left(0.2\right)\\ =4.2\end{array}$

Round off the value to the nearest integer.

  $E\left(X\right)=4$

Thus, the expected number of students who will run is 4

(b)

To determine

To find: The relative frequency table for 50 trials.

Answer to Problem 14PPS

The relative frequency table for 50 trials is shown in Table 1.

Explanation of Solution

Draw the possible table for 50 trials.

Prize, X	Frequency	P(X)
1	5	0.10
2	8	0.16
3	6	0.12
4	7	0.14
5	15	0.30
6	9	0.18

Table 1

Thus, the relative frequency table for 50 trials is shown in Table 1.

(c)

To determine

To find: The graph for experimental probability distribution.

Answer to Problem 14PPS

The graph for experimental probability distribution is shown in figure 1.

Explanation of Solution

From Table (1), the graph is plotted as,

  

Figure 1

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