Concept explainers
(a)
To find: The relative frequency table showing the theoretical probabilities.
(a)
Answer to Problem 5CYU
Therelative frequency table is shown in table 1
Explanation of Solution
Given:
The given figure is shown in Figure 1
Figure 1
Calculation:
Consider the random variable is X that represents the sum of the values of two spins of the spinning wheels.
The minimum value of the wheel is 2 and maximum is 12, the X can take any value 4 to 24. Thus, the even space of the random variable is,
Consider the definition of the theatrical probability as,
The random variable can take any value of 4 in one ways as 2 in spin 1 and 2 in spin 2.
The wheel spun the number that can appear are
And,
Hence,
Similarly the random variable X can take the value 6 in two ways as,
1st spin | 2 | 4 |
2nd spin | 4 | 2 |
Then, the probability is,
Similarly the random variable X can take the value 12 in two ways as,
1st spin | 2 | 5 | 4 | 8 | 6 | 10 | 2 |
2nd spin | 5 | 2 | 8 | 4 | 6 | 2 | 10 |
Then, the probability is,
Similarly the random variable X can take the value 20 in two ways as,
1st spin | 10 | 12 | 8 |
2nd spin | 10 | 8 | 12 |
Then, the probability is,
Thus, the relative frequency table is shown in Table 1
Table 1
Frequency | ||
4 | 1 | |
6 | 2 | |
7 | 2 | |
8 | 3 |
(b)
To find: The graph for the theoretical probability distribution.
(b)
Answer to Problem 5CYU
Thegraph is shown in Figure 1
Explanation of Solution
Calculation:
From the theoretical data shown in Table 1 the graph for the data is shown in Figure 2
Figure 2
(c)
To find: The relative frequency table for 100 trials.
(c)
Answer to Problem 5CYU
The relative frequency table is shown in table 2
Explanation of Solution
Perform 100 trials of the spinning the wheel two times and record the sum of the values and its frequency. The calculate the corresponding probability using the same concept as mentioned in part (a)
The required table is shown in Table 2
Table 2
Frequency | ||
4 | 1 | |
6 | 1 | |
7 | 3 | |
8 | 3 | |
9 | 2 | |
10 | 6 | |
11 | 5 | |
12 | 7 | |
13 | 5 | |
14 | 3 | |
15 | 3 | |
16 | 3 | |
17 | 4 | |
18 | 5 | |
19 | 2 | |
20 | 3 | |
22 | 2 | |
24 | 1 |
(d)
To find: The relative frequency table showing the theoretical probabilities.
(d)
Answer to Problem 5CYU
The relative frequency table is shown in table 1
Explanation of Solution
From the theoretical data shown in Table 1 the graph for the data is shown in Figure 3
Figure 3
(e)
To find: The expected value of the random variable X .
(e)
Answer to Problem 5CYU
Thevalue of the random variable is
Explanation of Solution
Consider the formula to determine the expected value of the random variable is,
Then,
(f)
To find: The standard deviation of the random variable X.
(f)
Answer to Problem 5CYU
The value of the standard deviation is
Explanation of Solution
Consider the formula to determine standard deviation of the random variable X is,
Therefore,
Chapter 11 Solutions
Glencoe Algebra 2 Student Edition C2014
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