Question

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50. what is the probability that a student uses fewer than 400 minutes

Answer 1

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

$theta = standard \: deviation$

and

$u = mean$

GIVEN

$x < 400 \: min$
$u = 500$
$theta = 50$

SOLVE

$z=\frac{x-u}{theta}=\frac{400-500}{50}=-2$

plug into equation written in the attached image and calculate...

$y = 0.02275$

Multiply by 100 to convert to percentage.

ANSWER

There is a 2.3% chance a student uses less than 400 minutes.