Let's start by addressing each question step-by-step:
### 1. What percentage of CEOs are 60 years or older?
To determine the percentage of CEOs who are 60 years old or older, we first need to ascertain the total number of CEOs who are in this age category. Looking at the provided age categories:
- Ages 65-69: 8 CEOs
- Ages 70-74: 1 CEO
So, the total number of CEOs who are 60 years or older is:
[tex]\[ 8 + 1 = 9 \][/tex]
The total number of CEOs considered is 892. Therefore, the percentage of CEOs who are 60 years or older is calculated as:
[tex]\[ \text{Percentage} = \left(\frac{9}{892}\right) \times 100 \][/tex]
After carrying out the calculation and rounding to the nearest tenth:
[tex]\[ \text{Percentage} \approx 1.0\% \][/tex]
### 2. What is the relative frequency of ages under 50?
The relative frequency for a given category is the ratio of the number of items in that category to the total number of items. For CEOs under the age of 50, the provided data breaks down the number of CEOs by five-year age bands (20-24, 25-29, 30-34, 35-39, 40-44, 45-49). Summing these numbers:
- 20-24: 4 CEOs
- 25-29: 29 CEOs
- 30-34: 42 CEOs
- 35-39: 84 CEOs
- 40-44: 128 CEOs
- 45-49: 224 CEOs
- Under 50 (sum of the above): 234 CEOs
Thus, the relative frequency is:
[tex]\[ \text{Relative frequency} = \frac{4 + 29 + 42 + 84 + 128 + 224 + 234}{892} \][/tex]
Upon calculation and rounding to the nearest hundredth:
[tex]\[ \text{Relative frequency} \approx 0.84 \][/tex]
### 3. What is the cumulative frequency for CEOs younger than 55?
For this question, to find the cumulative frequency, we sum up the frequencies of all age categories below 55. These age groups are:
- 20-24: 4 CEOs
- 25-29: 29 CEOs
- 30-34: 42 CEOs
- 35-39: 84 CEOs
- 40-44: 128 CEOs
- 45-49: 224 CEOs
- 50-54: 234 CEOs
Adding these numbers gives:
[tex]\[ \text{Cumulative frequency} = 4 + 29 + 42 + 84 + 128 + 224 + 234 \][/tex]
Upon adding these values:
[tex]\[ \text{Cumulative frequency} = 745 \][/tex]
### Summary of Answers:
1. Percentage of CEOs who are 60 years or older: 1.0%
2. Relative frequency of ages under 50: 0.84
3. Cumulative frequency for CEOs younger than 55: 745
Each answer has been calculated and rounded as per the required specifications.
