for a group experiment, your science class measured the fine-particulate concentrations in the air at random places around campus, and estimated a sample average of 22 μg/m3 (micrograms per cubic meter). if 144 readings were taken, and the standard deviation of the sample measurements was 4 μg/m3, you are 99.7% confident that actual concentration of fine particulates at the school is ________.

A. 21.3μg/m3 -22.7μg/m3
B. 21μg/m3- 23μg/m3
C. 18μg/m3-26μg/m3
D. 21.7μg/m3-22.3μg/m3

Question

for a group experiment, your science class measured the fine-particulate concentrations in the air at random places around campus, and estimated a sample average of 22 μg/m3 (micrograms per cubic meter). if 144 readings were taken, and the standard deviation of the sample measurements was 4 μg/m3, you are 99.7% confident that actual concentration of fine particulates at the school is ________.

A. 21.3μg/m3 -22.7μg/m3 
B. 21μg/m3- 23μg/m3 
C. 18μg/m3-26μg/m3 
D. 21.7μg/m3-22.3μg/m3

sillybilly123 · Answer

Sample mean: $\bar x = 22$

Standard Error: $SE \approx \dfrac{\text{Sample SD}}{\sqrt n} = \dfrac{4}{\sqrt{ 144}} = \dfrac{1}{3}$

Assunimg normal distribution of sample, you can be 99.7pc sure that actual mean concentration is in range $\bar x \pm 3 \cdot SE$

finish it yourself, yes?