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Daily screen time is a critical metric for understanding teenage behavior and well-being. A national health study investigates the amount of time teenagers spend on screens (e.g., phones, computers, TVs) per day. In 2023, the daily screen time of teenagers in a large sample was normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours.
Using this information, calculate the following probabilities or values for the daily screen time of teenagers:
  1. The percentage of teenagers with daily screen time between 4.5 and 6 hours.
    \(\pourcent\)
  2. The percentage of teenagers with daily screen time between 6 and 9 hours.
    \(\pourcent\)
  3. The percentage of teenagers with daily screen time less than 7.5 hours.
    \(\pourcent\)
  4. In 2024, if there were 1200 teenagers in this sample, estimate the number of teenagers with daily screen time greater than 9 hours. (
    ! e \(\pi\) ( ) % AC sin cos tan 7 8 9 / \(\sin^{-1}\) \(\cos^{-1}\) \(\tan^{-1}\) 4 5 6 * \(x^2\) \(\sqrt{\phantom{2}}\) xy 1 2 3 - ln exp log 0 . = +
    and round to the nearest integer.)
    teenagers
For a normal distribution, the coverage probabilities are illustrated below: