Question

there are 21 students in a class. thirteen of them are forestry students and 8 of them are natural resources management students. the mean commute time of the forestry students is 57.7 minutes, and the mean commute time of all 21 students is 67.9 minutes. what is the mean commute time of the natural resources management students? round your answer to one decimal place.
the mean commute time of natural resources management students, rounded to one decimal place, is minutes.

Explanation:

Step1: Calculate total commute time of all students

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, so the total commute - time of all 21 students is $n\times\bar{x}=21\times67.9 = 1425.9$ minutes.

Step2: Calculate total commute time of Forestry students

The total commute - time of 13 Forestry students with a mean of 57.7 minutes is $13\times57.7=750.1$ minutes.

Step3: Calculate total commute time of Natural Resources Management students

Let the total commute - time of Natural Resources Management students be $T$. Then $T = 1425.9−750.1 = 675.8$ minutes.

Step4: Calculate the mean commute time of Natural Resources Management students

There are 8 Natural Resources Management students. The mean $\bar{y}=\frac{T}{8}=\frac{675.8}{8}=84.5$ minutes.

Answer:

84.5