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Intelligence Quotient (IQ) scores are widely used to measure cognitive ability. A psychological research institute analyzes IQ scores to understand population intelligence distributions. In 2023, the IQ scores of a large adult population were normally distributed with a mean of 100 and a standard deviation of 15.
Using this information, calculate the following probabilities or values for the IQ scores:
  1. The percentage of adults with IQ scores between 85 and 100.
    \(\pourcent\)
  2. The percentage of adults with IQ scores between 70 and 100.
    \(\pourcent\)
  3. The percentage of adults with IQ scores less than 115.
    \(\pourcent\)
  4. In 2024, if there were 800 adults in this population, estimate the number of adults with IQ scores greater than 130. (
    ! 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.)
    adults
For a normal distribution, the coverage probabilities are illustrated below: