Question

Among U.S. adolescents ages 12-17, the amount of time (in minutes per week) spent listening to streaming audio media (music, podcasts, etc.) is Normally distributed with a mean of 247 minutes and a standard deviation of 103 minutes. Based on this information, what percentage of a random sample of 500 U.S. adolescents ages 12-17 listen to more than 180 minutes of streaming media each week

Answer 1

74.23% of a random sample of 500 U.S. adolescents ages 12-17 listen to more than 180 minutes of streaming media each week.

Explanation:

We are given the following information in the question:

Mean, μ = 247 minutes

Standard Deviation, σ = 103 minutes

Sample size,n = 500

We are given that the distribution of time is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(more than 180 minutes)

P(x > 180)

`P( x > 180) = P( z > \displaystyle(180 - 247)/(103)) = P(z > -0.6504)`

`= 1 - P(z \leq -0.6504)`

Calculation the value from standard normal z table, we have,

`P(x > 180) = 1 - 0.2577 = 0.7423= 74.23\%`

74.23% of a random sample of 500 U.S. adolescents ages 12-17 listen to more than 180 minutes of streaming media each week.