Question

the following data represents the age of 30 lottery winners. given the frequency distribution for the data,

age	frequency	relative frequency
20 - 29	3	0.1
30 - 39	5	0.1667
40 - 49	7	0.2333
50 - 59	3	0.1
60 - 69	8	0.2667
70 - 79	3	0.1
80 - 89	1	0.0333

what is the frequency of lottery winners of age between 19 and 40?
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what percentage of lottery winners are 70 years or older?
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Explanation:

First Sub - Question: Frequency of lottery winners of age between 19 and 40

Step1: Identify relevant age groups

The age groups between 19 and 40 are 20 - 29 and 30 - 39.

Step2: Find frequencies of these groups

The frequency for 20 - 29 is 3, and for 30 - 39 is 5.

Step3: Sum the frequencies

To find the total frequency, we add the two frequencies: $3 + 5=8$.

Step1: Identify relevant age groups

The age groups 70 years or older are 70 - 79 and 80 - 89.

Step2: Find relative frequencies of these groups

The relative frequency for 70 - 79 is 0.1, and for 80 - 89 is 0.0333.

Step3: Sum the relative frequencies

First, add the relative frequencies: $0.1+ 0.0333 = 0.1333$.

Step4: Convert to percentage

To convert to a percentage, multiply by 100: $0.1333\times100 = 13.33\%$ (rounded to two decimal places, or we can also calculate using frequencies. The frequency for 70 - 79 is 3 and for 80 - 89 is 1. Total frequency for 70+ is $3 + 1=4$. The total number of winners is 30. So percentage is $\frac{4}{30}\times100\approx13.33\%$).

Answer:

8

Second Sub - Question: Percentage of lottery winners who are 70 years or older