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=(x-u)/(theta)=(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.