Answer:
(a) and (c)
Step-by-step explanation:
Given
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Required
Select all true statements
First, calculate the total observed frequency;
[tex]Total = 11 + 16 + 14 + 20 + 12 + 17[/tex]
[tex]Total = 90[/tex]
(a): Relative frequency of 4 is 2/9
Relative frequency is calculated by:
[tex]RF= \frac{Observed\ Frequency}{Total}[/tex]
For roll 4
[tex]Observed\ frequency = 20[/tex]
So, the relative frequency is:
[tex]RF = \frac{20}{90}[/tex]
Simplify
[tex]RF = \frac{2}{9}[/tex]
(a) is true
(b): Experimental probability of 3 greater than its theoretical probability
The experimental probability is its relative frequency;
For roll 3
[tex]Observed\ frequency = 14[/tex]
The experimental probability is:
[tex]Pr = \frac{14}{90}[/tex]
Simplify
[tex]Pr = \frac{7}{45} = 0.156[/tex]
To calculate the theoretical probability, w have:
[tex]S = \{1,2,3,4,5,6\}[/tex] ---- sample space
[tex]n(S)= 6[/tex]
[tex]n(3) = 1[/tex] --- number of times 3 occur
The theoretical probability is:
[tex]Pr = \frac{1}{6} = 0.167[/tex]
The theoretical probability is [tex]greater\ than\ the[/tex] experimental probability.
(b) is false
(c): Experimental probability of 2 greater than its theoretical probability
Using the explanations in (b), we have:
For roll 2
[tex]Observed\ frequency = 16[/tex]
The experimental probability is:
[tex]Pr = \frac{16}{90}[/tex]
Simplify
[tex]Pr = \frac{8}{45} = 0.178[/tex]
To calculate the theoretical probability, we have:
[tex]n(S)= 6[/tex]
[tex]n(2) = 1[/tex]
The theoretical probability is:
[tex]Pr = \frac{1}{6} = 0.167[/tex]
The experimental probability is [tex]greater\ than\ the[/tex] theoretical probability.
(c) is true
(d): Relative frequency of 5 is 2/13
For roll 5
[tex]Observed\ frequency = 12[/tex]
The relative frequency is:
[tex]RF = \frac{12}{90}[/tex]
Simplify
[tex]RF = \frac{2}{15}[/tex]
(d) is true
