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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

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sdgismep6d4p4
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.
Ver imagen sdgismep6d4p4

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