Questions: The data set below represents the ages of 36 executives. Find the percentile that corresponds to an age of 42 years old. 37 29 30 33 33 34 34 36 37 37 45 40 41 41 41 42 43 43 43 45 50 52 52 53 58 60 60 61 61 61 62 63 63 64 66 66 Percentile of 42= 38 (Round to the nearest integer as needed.)

Solution Steps

The ages of the 36 executives are organized as follows:

\[ \text{Ages} = [29, 30, 33, 33, 34, 34, 36, 37, 37, 37, 40, 41, 41, 41, 42, 43, 43, 43, 45, 45, 50, 52, 52, 53, 58, 60, 60, 61, 61, 61, 62, 63, 63, 64, 66, 66] \]

To find the percentile corresponding to an age of \(42\) years, we count the number of executives whose ages are less than or equal to \(42\):

• Count of ages \( \leq 42 \): \( 15 \)
• Total number of executives: \( 36 \)

The percentile is calculated using the formula:

\[ \text{Percentile} = \left( \frac{\text{Count of values} \leq 42}{\text{Total count}} \right) \times 100 \]

Substituting the values:

\[ \text{Percentile} = \left( \frac{15}{36} \right) \times 100 \approx 41.67 \]

Rounding to the nearest integer gives us \(42\).

Final Answer