Calculate normal probabilities, an inverse quantile and represent a shaded region.
Calculate normal probabilities, an inverse quantile and represent a shaded region.
6 marks
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The weights of a group of children are normally distributed with a mean of 22.5 kg and a standard deviation of 2.2 kg.
Write down the probability that a child selected at random has a weight more than 25.8 kg.
Of the group 95% weigh less than k kilograms. Find the value of k.
The diagram below shows a normal curve. On the diagram, shade the region that represents the following information: 87% of the children weigh less than 25 kg
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Answer:The 95th percentile is \(k=22.5+2.2z_{0.95}=26.1\) kg. For the final diagram, shade the region to the left of 25 kg and label its area 0.87.