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Height and weight are key measurements for tracking a child’s development. The World Health Organization assesses child development by comparing the weights of children of the same height and gender. In 2009, the weights of all 80 cm girls in a reference population were normally distributed with a mean of 10.2 kg and a standard deviation of 0.8 kg.
Using this information, calculate the following probabilities or values for the weights of 80 cm girls:
  1. The percentage of girls with weights between 10.2 kg and 11 kg.
    \(\pourcent\)
  2. The percentage of girls with weights between 10.2 kg and 11.8 kg.
    \(\pourcent\)
  3. The percentage of girls with weights greater than 9.4 kg.
    \(\pourcent\)
  4. In 2010, if there were 545 girls who were 80 cm tall, estimate the number of girls with weights between 9.4 kg and 11 kg. (
    ! 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.)
    girls
For a normal distribution, the coverage probabilities are illustrated below: