Question

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

age	frequency	relative frequency	cumulative relative frequency
20,29	3	0.1	0.1
30,39	5	0.1667	0.2667
40,49	5	0.1667	0.4334
50,59	7	0.2333	0.6667
60,69	6	0.2	0.8667
70,79	3	0.1	0.9667
80,89	1	0.0333	1

a) what is the frequency of lottery winners of age between 19 and 40?
b) what percentage of lottery winners are 70 years or older?
c) what is the relative frequency of ages under 40?
d) what is the cumulative relative frequency of lottery winners younger than 50?
e) which graph shows the relative frequency?

Explanation:

Step1: Identify relevant intervals for part a

The intervals relevant for ages between 19 and 40 are [20,29] and [30,39].

Step2: Sum frequencies for part a

Add the frequencies of [20,29] and [30,39]. $3 + 5=8$.

Step3: Identify relevant intervals for part b

The intervals relevant for ages 70 or older are [70,79] and [80,89].

Step4: Calculate percentage for part b

Sum relative - frequencies: $0.1+0.0333 = 0.1333$. Convert to percentage: $0.1333\times100 = 13.33\%$.

Step5: Identify relevant intervals for part c

The intervals relevant for ages under 40 are [20,29] and [30,39].

Step6: Sum relative - frequencies for part c

$0.1 + 0.1667=0.2667$.

Step7: Identify relevant intervals for part d

The intervals relevant for ages younger than 50 are [20,29], [30,39], and [40,49].

Step8: Find cumulative relative - frequency for part d

From the table, the cumulative relative - frequency for ages up to 49 is 0.4334.

Answer:

a) 8
b) 13.33
c) 0.2667
d) 0.4334
e) (No graphs provided, so cannot answer this part)