A business has 28 employees. Their ages, in years, are given below. 32 41 57 64 19 21 35 18 43 54 63 65 33 22 39 58 18 42 20 34 21 49 33 55 34 57 43 63 KEY: 1|9 = 19 years of age. (a) Complete the stem-and-leaf diagram, showing the ages of all 28 employees. (b) Find the percentage of employees who are older than 40 years of age. (c) One employee is chosen at random on a day when all employees are present at work. (i) Find the probability that the employee is a teenager (<20 years of age). (ii) Find the probability that the employee chosen is a person in their thirties whose age is even or a person in their forties whose age is odd.

Leaving Cert Mathematics Statistics & Data: A business has 28 employees. The

A business has 28 employees - Leaving Cert Mathematics - Question 1 - 2019

Question 1

A business has 28 employees. Their ages, in years, are given below. 32 41 57 64 19 21 35 18 43 54 63 65 33 22 39 58 18 42 20 34 21 49 33 55 34 ... show full transcript

Worked Solution & Example Answer:A business has 28 employees - Leaving Cert Mathematics - Question 1 - 2019

Step 1

Complete the stem-and-leaf diagram, showing the ages of all 28 employees.

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Answer

To construct the stem-and-leaf diagram, we separate each age into a stem and a leaf. The stem represents the tens digit(s), while the leaf represents the units digit.

Here’s how the ages can be organized:

1 | 8 8 9
2 | 1 1 2 3 3
3 | 2 4 4 5 5
4 | 1 3 3 9
5 | 7 7
6 | 3 4 5
7 |
8 |
9 |

This diagram clearly displays the age distribution among the employees.

Step 2

Find the percentage of employees who are older than 40 years of age.

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Answer

To find the percentage, first, identify the number of employees older than 40:

Ages > 40: 41, 54, 63, 65, 43, 58, 49, 55, 57, 43 (10 employees)

Total employees = 28.

The percentage is calculated as:

$ext{Percentage} = \left( \frac{10}{28} \right) \times 100 = 35.71\%$ .

Thus, the percentage of employees older than 40 years is approximately 36%.

Step 3

Find the probability that the employee is a teenager (<20 years of age).

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Answer

Count the number of teenagers from the age data:

Teenagers: 18, 18, 19 (3 employees).

The total number of employees is 28.

The probability is:

$P(\text{teenager}) = \frac{3}{28}$ .

Step 4

Find the probability that the employee chosen is a person in their thirties whose age is even or a person in their forties whose age is odd.

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Answer

First, identify employees in their thirties whose ages are even:

Thirties (even): 32, 34, 34 (3 employees).

Next, identify employees in their forties whose ages are odd:

Forties (odd): 41, 43, 43 (3 employees).

Total qualifying employees = 3 (thirties) + 3 (forties) = 6.

The probability is calculated as:

$P(\text{even thirties or odd forties}) = \frac{6}{28} = \frac{3}{14}$ .

A business has 28 employees - Leaving Cert Mathematics - Question 1 - 2019

Worked Solution & Example Answer:A business has 28 employees - Leaving Cert Mathematics - Question 1 - 2019

Complete the stem-and-leaf diagram, showing the ages of all 28 employees.

Find the percentage of employees who are older than 40 years of age.

Find the probability that the employee is a teenager (<20 years of age).

Find the probability that the employee chosen is a person in their thirties whose age is even or a person in their forties whose age is odd.

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