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.
![\text{Percentile rank of x}=\frac{\text{Number of values below x}}{\text{Total number of data points}}\times 100](https://tex.z-dn.net/?f=%5Ctext%7BPercentile%20rank%20of%20x%7D%3D%5Cfrac%7B%5Ctext%7BNumber%20of%20values%20below%20x%7D%7D%7B%5Ctext%7BTotal%20number%20of%20data%20points%7D%7D%5Ctimes%20100)
![\text{Percentile rank of 41}=0.361111\times 100](https://tex.z-dn.net/?f=%5Ctext%7BPercentile%20rank%20of%2041%7D%3D0.361111%5Ctimes%20100)
![\text{Percentile rank of 41}=36.11\approx 37](https://tex.z-dn.net/?f=%5Ctext%7BPercentile%20rank%20of%2041%7D%3D36.11%5Capprox%2037)
Therefore, the percentile rank that corresponds to age of 41 years old is 37th percentile.