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
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
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 30E
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answer part b) and c)
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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F14bace20-f9b4-49a2-9b7a-1902c2a78ab2%2Fc188794c-2212-47d6-a345-08d5bebe8138%2Fstc4zll_processed.jpeg&w=3840&q=75)
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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