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