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Answer:
37th percentile.
Step-by-step explanation:
We have been given a data set that represents the ages of 36 executives. We are asked to find the percentile that corresponds to an age of 41 years.
28, 29, 29, 32, 32, 33, 34, 34, 34, 34, 37, 37, 38, 41, 41, 42, 45, 45, 47, 47, 47, 48, 50, 51, 53, 56, 56, 56, 61, 61, 62, 63, 64, 64, 65, 66.
Let us count the number of data points below and at 41.
We can see that the number of data points at and below 41 is 13.
We will use percentile formula to solve our given problem.
[tex]\text{Percentile rank of x}=\frac{\text{Number of values below x}}{\text{Total number of data points}}\times 100[/tex]
[tex]\text{Percentile rank of 41}=\frac{13}{36}\times 100[/tex]
[tex]\text{Percentile rank of 41}=0.361111\times 100[/tex]
[tex]\text{Percentile rank of 41}=36.11\approx 37[/tex]
Therefore, the percentile rank that corresponds to age of 41 years old is 37th percentile.
The percentile that corresponds to an age of 41 years old is the 37th percentile.
What is a percentile?
Percentile is a measure of a dataset below which a percentage in its frequency distribution falls.
Given
The data set below represents the ages of 36 executives.
28, 29, 29, 32, 32, 33, 34, 34, 34, 34, 37, 37, 38, 41, 41, 42, 45, 45, 47, 47, 47, 48, 50, 51, 53, 56, 56, 56, 61, 61, 62, 63, 64, 64, 65, 66.
The percentile corresponds to an age of 41 years old is given by the following formula;
[tex]\rm Percentile = \dfrac{Total \ number \ of \ values}{Total \ number \ of \ data \ points}\times 100\\\\ Percentile =\dfrac{13}{36}\times 100\\\\Percentile=\dfrac{1300}{36}\\\\Percentile=37[/tex]
Hence, the percentile that corresponds to an age of 41 years old is the 37th percentile.
To learn more about Percentile click the link given below.
https://brainly.com/question/25105743
