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 between 400 and 500 minutes?

Answer 1

Let X be the number of cell phone minutes used by high school seniors.

X follows Normal distribution with mean μ = 500 and standard deviation σ =50.

The probability that students uses between 400 and 500 minutes is

P(400 < X < 500) = $P(\frac{400-500}{50} < \frac{x -mean}{standard deviation} < \frac{500-500}{50} )$

= P( -2 < Z < 0)

= P(Z < 0) - P(Z < -2)

= 0.5 - 0.0228

P(400 < X < 500) = 0.4772

The probability that student uses between 400 and 500 minutes is 0.4772