a) An ecologist wishes to mark off a circular sampling region having radius 10 m. However, the radius of the resulting region is actually a random variable R with pdf [1 - (10 – r)²] 9

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a) An ecologist wishes to mark off a circular sampling region having radius 10 m. However, the<br>radius of the resulting region is actually a random variable R with pdf<br>[1 - (10 – r)²] 9<rs 11<br>%3D<br>= (4))<br>otherwise<br>What is the expected area of the resulting circular region?<br>b) 90% of students at school are between 1.1m and 1.7m tall. Assuming this data is normally<br>distributed can you calculate the mean and standard deviation?<br>c) Let X denote the 1Q (as determined by the Stanford-Binet Intelligence Quotient Test) of a<br>randomly selected Kenyan. It has long been known that X follows a normal distribution with<br>mean 100 and standard deviation of 16. A program is recruiting the topmost 8% of intelligent<br>Kenyans. What is the lowest 1Q mark for a Kenyan to score to be included in the program?<br>

Extracted text: a) An ecologist wishes to mark off a circular sampling region having radius 10 m. However, the radius of the resulting region is actually a random variable R with pdf [1 - (10 – r)²] 9

Jun 04, 2022

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a) An ecologist wishes to mark off a circular sampling region having radius 10 m. However, the radius of the resulting region is actually a random variable R with pdf [1 - (10 – r)²] 9

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