c. What is the relative frequency of ages 40 to 49 ? d. What is the cumulative relative frequency of lottery winners younger than 50 ? e. How many lottery winners were between 60 and 69 years old?

Below is one acceptable way to answer these questions. (Any answer equivalent to the answer below is correct.) In many problems the age‐distribution of lottery winners is given in a frequency table. For example, suppose that the table below was given:   Age Range   Frequency   20–29     5   30–39     12   40–49     9   50–59     8   60–69     6   70–79     4     Total    44 Then we can answer parts (c), (d), and (e) as follows: ──────────────────────────── c. What is the relative frequency of ages 40 to 49?  To get the relative frequency of any group, we divide its frequency by the total number. Here the frequency for ages 40–49 is 9 and the total is 44. Therefore,   Relative frequency = 9/44 ≈ 0.2045 or about 20.5%. ──────────────────────────── d. What is the cumulative relative frequency of lottery winners younger than 50?  “Lottery winners younger than 50” means we add the frequencies for all age groups with upper limits less than 50. In our table these are 20–29, 30–39, and 40–49. Their frequencies add up to:   5 + 12 + 9 = 26.  Then the cumulative relative frequency is   26/44 ≈ 0.5909 or about 59.1%. ──────────────────────────── e. How many lottery winners were between 60 and 69 years old?  This count is given directly by the frequency for the age group 60–69. In our example that is 6 winners. ──────────────────────────── Keep in mind that the actual numbers will depend on the data provided. In general you would do the following:  • (c) Relative frequency for 40–49 = (Frequency for 40–49) / (Total frequency)  • (d) Cumulative relative frequency for winners younger than 50 = (Frequency for 20–29 + Frequency for 30–39 + Frequency for 40–49) / (Total frequency)  • (e) The number of winners between 60 and 69 is simply the frequency for that age group. Any answer that shows how to compute the answers in this way (and gives equivalent numerical values when using the data from your frequency distribution) is correct.