A sheet on the normal distribution using rules of thumb for proportions within 1, 2 or 3 standard deviations of the mean. There are three diagrams: one showing 68% of the distribution within 1 sd, a second showing 95% of the distribution within 2sd, and a third showing almost 100% within 3sd. Then there are 4 questions:
1. Masses of adult females of a species of dolphin are normally distributed with mean 220 kg and standard deviation 18 kg. What proportion of female dolphins of this species are between
202 kg and 256 kg in weight?
2. Heights of leprechauns are normally distributed with a mean of 1.2 m. 16 % of leprechauns are over 1.3 m tall. What proportion of leprechauns are under 1 m tall?
3. Harriet is studying a species of lizard. 2.5 % of them have masses under 20g, and 16 % of them have masses over 38 g. What is the mean mass of the lizards, assuming that their masses are normally distributed?
4. Harshant measures the heights of 400 sixteen year old boys. The tallest is 191 cm tall and the shortest is 158 cm tall. Estimate the probability that a randomly selected sixteen year old boy is between 169 cm and 180 cm tall. What assumptions are needed for this estimate to be valid?
Normal distributions in #CoreMaths this week. I like the approach of introducing calculations using the proportions within 1, 2 or 3 standard deviations of the mean to begin with. And thanks to @catrionaagg.bsky.social I always label inflection points.
#MathsToday
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