Question

an environmental scientist is investigating the volatility of 175 organic compounds by finding the boiling point of each compound. the mean boiling point of all 175 compounds is 167 degrees celsius. the scientist classifies each of these compounds as either semivolatile or volatile. of the 175 compounds, 50 compounds were classified as semivolatile, and these 50 compounds have a mean boiling point of 322 degrees celsius. the remaining 125 compounds were classified as volatile. what is the mean boiling point, in degrees celsius, of the 125 compounds classified as volatile compounds? enter your numerical answer enter your answer... enter your answer as a number, fraction, or decimal question 14 of 22 math - module2 question navigator english - module1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 leaked sat exams

Explanation:

Step1: Find the total boiling - point of all 175 compounds

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $\bar{x}$ is the mean, $n$ is the number of data - points, and $\sum_{i = 1}^{n}x_{i}$ is the sum of the data - points. Given $n = 175$ and $\bar{x}=167$, the total boiling - point of all 175 compounds is $175\times167 = 29225$.

Step2: Find the total boiling - point of the 50 semivolatile compounds

Given $n_1 = 50$ and $\bar{x}_1=322$, the total boiling - point of the 50 semivolatile compounds is $50\times322=16100$.

Step3: Find the total boiling - point of the 125 volatile compounds

Let the total boiling - point of the 125 volatile compounds be $T$. We know that the total boiling - point of all 175 compounds is the sum of the total boiling - point of the 50 semivolatile compounds and the total boiling - point of the 125 volatile compounds. So $T=29225 - 16100=13125$.

Step4: Find the mean boiling - point of the 125 volatile compounds

Using the mean formula $\bar{x}_2=\frac{T}{125}$, substituting $T = 13125$ and $n_2 = 125$, we get $\bar{x}_2=\frac{13125}{125}=105$.

Answer:

105