Question

select the correct answer.

the speed of nitrogen molecules in the atmosphere (at \\(20^\circ\text{c}\\)) 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?

\\(\bigcirc\\) 84% of the molecules have speeds between 450 meters/second and 550 meters/second.
\\(\bigcirc\\) 68% of the molecules have speeds between 450 meters/second and 550 meters/second.
\\(\bigcirc\\) 50% of the molecules have speeds between 450 meters/second and 550 meters/second.
\\(\bigcirc\\) 34% of the molecules have speeds greater than 550 meters/second.

Explanation:

Identify parameters and interval

$$
LATEXBLOCK0
$$

Calculate z-scores for the interval boundaries

$$
LATEXBLOCK1
$$

Apply the Empirical Rule

$$ P(-1 \le Z \le 1) \approx 0.68 \implies 68\% $$

Answer:

• 84% of the molecules have speeds between 450 meters/second and 550 meters/second.
• 68% of the molecules have speeds between 450 meters/second and 550 meters/second. (Correct answer)
• 50% of the molecules have speeds between 450 meters/second and 550 meters/second.
• 34% of the molecules have speeds greater than 550 meters/second.