Answer:
(a) See attachment for table
(b) ![Atmost\ 6 = 21.667\%](https://tex.z-dn.net/?f=Atmost%5C%206%20%3D%2021.667%5C%25)
(c) ![Less\ than\ 6 = 21.667\%](https://tex.z-dn.net/?f=Less%5C%20than%5C%206%20%3D%2021.667%5C%25)
(d) ![At\ least\ 6 = 78.333\%](https://tex.z-dn.net/?f=At%5C%20least%5C%206%20%3D%2078.333%5C%25)
Step-by-step explanation:
Given
The data (in the question)
Solving (a): Frequency and Relative frequencies of each data
The range of the data is 0 to 8. So the frequency of each is the number of times each of 0 - 8 occurs.
This is tabulated below:
![\begin{array}{ccc}x & {Frequency} & {Relative\ Frequency} & {0} & {7} & {11.667\%} &{1}& {13} & {21.667\%} & {2} & {13} & {21.667\%} & {3} & {14} &{23.333\%} & {4} & {5} & {8.333\%} & {5} &{3} &{5.000\%} &{6} &{2} & {3.333\%} & {7} & {2} & {3.333\%} & {8} & {1} & {1.667\%} \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccc%7Dx%20%26%20%7BFrequency%7D%20%26%20%7BRelative%5C%20Frequency%7D%20%26%20%7B0%7D%20%26%20%7B7%7D%20%26%20%7B11.667%5C%25%7D%20%26%7B1%7D%26%20%7B13%7D%20%26%20%7B21.667%5C%25%7D%20%26%20%7B2%7D%20%26%20%7B13%7D%20%26%20%7B21.667%5C%25%7D%20%26%20%7B3%7D%20%26%20%7B14%7D%20%26%7B23.333%5C%25%7D%20%26%20%7B4%7D%20%26%20%7B5%7D%20%26%20%7B8.333%5C%25%7D%20%26%20%7B5%7D%20%26%7B3%7D%20%26%7B5.000%5C%25%7D%20%26%7B6%7D%20%26%7B2%7D%20%26%20%7B3.333%5C%25%7D%20%26%20%7B7%7D%20%26%20%7B2%7D%20%26%20%7B3.333%5C%25%7D%20%26%20%7B8%7D%20%26%20%7B1%7D%20%26%20%7B1.667%5C%25%7D%20%20%5C%20%5Cend%7Barray%7D)
![Total\ \ \ 60](https://tex.z-dn.net/?f=Total%5C%20%5C%20%5C%2060)
The relative frequency is calculated as:
![Relative\ Frequency = \frac{Frequency}{Total\ Frequency} * 100\%](https://tex.z-dn.net/?f=Relative%5C%20Frequency%20%3D%20%5Cfrac%7BFrequency%7D%7BTotal%5C%20Frequency%7D%20%2A%20100%5C%25)
For instance: When x = 0:
![Relative\ Frequency = \frac{7}{60} * 100\%](https://tex.z-dn.net/?f=Relative%5C%20Frequency%20%3D%20%5Cfrac%7B7%7D%7B60%7D%20%2A%20100%5C%25)
![Relative\ Frequency = \frac{700}{60} * \%](https://tex.z-dn.net/?f=Relative%5C%20Frequency%20%3D%20%5Cfrac%7B700%7D%7B60%7D%20%2A%20%5C%25)
![Relative\ Frequency = 11.667 \%](https://tex.z-dn.net/?f=Relative%5C%20Frequency%20%3D%2011.667%20%5C%25)
Solving (b): Proportion that have at most 6.
Here, we consider frequencies of 0 to 6.
This is represented as thus:
![\begin{array}{ccc}x & {Frequency} & {Relative\ Frequency} & {4} & {5} & {8.333\%} & {5} &{3} &{5.000\%} &{6} &{2} & {3.333\%} & {7} & {2} & {3.333\%} & {8} & {1} & {1.667\%} \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccc%7Dx%20%26%20%7BFrequency%7D%20%26%20%7BRelative%5C%20Frequency%7D%20%26%20%20%7B4%7D%20%26%20%7B5%7D%20%26%20%7B8.333%5C%25%7D%20%26%20%7B5%7D%20%26%7B3%7D%20%26%7B5.000%5C%25%7D%20%26%7B6%7D%20%26%7B2%7D%20%26%20%7B3.333%5C%25%7D%20%26%20%7B7%7D%20%26%20%7B2%7D%20%26%20%7B3.333%5C%25%7D%20%26%20%7B8%7D%20%26%20%7B1%7D%20%26%20%7B1.667%5C%25%7D%20%20%5C%20%5Cend%7Barray%7D)
Add up the relative frequencies to get the proportion
![Atmost\ 6 = 8.333\% + 5.000\% + 3.333\% + 3.333\% + 1.667\%](https://tex.z-dn.net/?f=Atmost%5C%206%20%3D%208.333%5C%25%20%2B%205.000%5C%25%20%2B%203.333%5C%25%20%2B%203.333%5C%25%20%2B%201.667%5C%25)
![Atmost\ 6 = 21.667\%](https://tex.z-dn.net/?f=Atmost%5C%206%20%3D%2021.667%5C%25)
Solving (c): Proportion that have at fewer than 6.
Here, we consider frequencies of 0 to 5.
This is represented as thus:
![\begin{array}{ccc}x & {Frequency} & {Relative\ Frequency} & {4} & {5} & {8.333\%} & {5} &{3} &{5.000\%} &{6} &{2} & {3.333\%} & {7} & {2} & {3.333\%} & {8} & {1} & {1.667\%} \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccc%7Dx%20%26%20%7BFrequency%7D%20%26%20%7BRelative%5C%20Frequency%7D%20%26%20%20%7B4%7D%20%26%20%7B5%7D%20%26%20%7B8.333%5C%25%7D%20%26%20%7B5%7D%20%26%7B3%7D%20%26%7B5.000%5C%25%7D%20%26%7B6%7D%20%26%7B2%7D%20%26%20%7B3.333%5C%25%7D%20%26%20%7B7%7D%20%26%20%7B2%7D%20%26%20%7B3.333%5C%25%7D%20%26%20%7B8%7D%20%26%20%7B1%7D%20%26%20%7B1.667%5C%25%7D%20%20%5C%20%5Cend%7Barray%7D)
Add up the relative frequencies to get the proportion
![Less\ than\ 6 = 8.333\% + 5.000\% + 3.333\% + 3.333\% + 1.667\%](https://tex.z-dn.net/?f=Less%5C%20than%5C%206%20%3D%208.333%5C%25%20%2B%205.000%5C%25%20%2B%203.333%5C%25%20%2B%203.333%5C%25%20%2B%201.667%5C%25)
![Less\ than\ 6 = 21.667\%](https://tex.z-dn.net/?f=Less%5C%20than%5C%206%20%3D%2021.667%5C%25)
Solving (d): Proportion that have at least 6.
Here, we make use of the complement rule:
![At\ least\ 6 = 100\% - Less\ than\ 6](https://tex.z-dn.net/?f=At%5C%20least%5C%206%20%3D%20100%5C%25%20-%20Less%5C%20than%5C%206)
![At\ least\ 6 = 100\% - 21.667\%](https://tex.z-dn.net/?f=At%5C%20least%5C%206%20%3D%20100%5C%25%20-%2021.667%5C%25)
![At\ least\ 6 = 78.333\%](https://tex.z-dn.net/?f=At%5C%20least%5C%206%20%3D%2078.333%5C%25)