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 **(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 Probability: 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 57 43 63 **(a)** Com... 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 complete the stem-and-leaf diagram, we first organize the ages into stems and leaves. The stem represents the first digits of the ages, while the leaves represent the final digit.

Stem-and-Leaf Diagram:

Stem | Leaf
-----|------
  1  | 8 9
  2  | 1
  3  | 2 3 4 5 8
  4  | 1 3 9
  5  | 3 4 7
  6  | 3 4 5

In this diagram, the ages like 19 are represented as '1 | 9', and the complete ages can be read as 18, 19, 21, 32, etc.

Step 2

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

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Answer

To find the percentage of employees older than 40 years, we first count the employees who fit this criterion:

Employees older than 40: 41, 57, 64, 43, 54, 63, 65, 58, 42, 49, 55, 43, 63.
Total count: 14

Next, we calculate the percentage:

$\text{Percentage} = \left( \frac{14}{28} \right) \times 100 = 50\%$

Step 3

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

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Answer

To determine the probability of selecting a teenager:

Count of teenagers (ages < 20): 18, 19 = 2
Total employees: 28

Thus, the probability is:

$P(\text{teenager}) = \frac{2}{28} = \frac{1}{14}$

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, we identify the relevant groups.

Employees in their thirties (even ages): 32, 34 = 2
Employees in their forties (odd ages): 41, 43, 49 = 3

Total favorable outcomes = 2 (thirties) + 3 (forties) = 5.

Now, the total possible outcomes are still 28.

Thus, the probability is:

$P(\text{(thirties even) or (forties odd)}) = \frac{5}{28}$

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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