Answer:
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.
Step-by-step 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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(more than 180 minutes)
P(x > 180)
[tex]P( x > 180) = P( z > \displaystyle\frac{180 - 247}{103}) = P(z > -0.6504)[/tex]
[tex]= 1 - P(z \leq -0.6504)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 180) = 1 - 0.2577 = 0.7423= 74.23\%[/tex]
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.
