The speed of nitrogen molecules in the atmosphere (at 20ºC) follows a normal distribution with a mean speed of 500 meters/second
and a standard deviation of 50 meters/second. Which conclusion does this information best support? A. 84% of the molecules have speeds between 450 meters/second and 550 meters/second.
B. 68% of the molecules have speeds between 450 meters/second and 550 meters/second.
C. 50% of the molecules have speeds between 450 meters/second and 550 meters/second.
D. 34% of the molecules have speeds greater than 550 meters/second.
B. 68% of the molecules have speeds between 450 meters/second and 550 meters/second.
Step-by-step explanation:
Since there is a standard deviation of 50 meters per second, and the mean speed is 500 meters per second, the speeds would range between 500 - 50 meters per second and 500 + 50 meters per second, which would be a range of 450 to 550 meters per second.
If you remember the Empirical Rule (68-95-99), things that are one standard deviation from the mean are within 68% of the data. Two standard deviations would include 95% of the data. Three standard deviations would include 99% of the data. Since this question just covers one standard deviation, 68% of the molecules have speeds between 450 meters per second and 550 meters per second.
In order to find the distance between any two points, you must use the distance formula. when you plug in the points into the formula you end up with 8.246, rounded to the nearest tenth would be 8.2. I hope this helps!