Cumulative distribution function is written in the attached image. We know it's cumulative because the question asks sum of probabilities up to 400 minutes of cell phone usage.
where
[tex]theta = standard \: deviation[/tex]
and
[tex]u = mean[/tex]
GIVEN
[tex]x < 400 \: min[/tex]
[tex]u = 500[/tex]
[tex]theta = 50[/tex]
SOLVE
[tex]z=\frac{x-u}{theta}=\frac{400-500}{50}=-2[/tex]
plug into equation written in the attached image and calculate...
[tex]y = 0.02275[/tex]
Multiply by 100 to convert to percentage.
ANSWER
There is a 2.3% chance a student uses less than 400 minutes.
