A biologist captures 20 grizzly bears during the spring, and
fits each with a radio collar. At the end of summer, the biologist
is to observe 15 grizzly bears from a helicopter, and count the
number that are radio collared. This count is represented by the
random variable X.
Suppose there are 109 grizzly bears in the population.
(a) What is the probability that of the 15 grizzly bears observed, 4 had radio collars? Use four decimals in your answer.
(b) Find the probability that between 4
and 9 (inclusive) of the 15 grizzly bears observed were radio
P(4≤ X ≤9)=
(c) How many of the 15 grizzly bears
observe from the helicopter does the biologist expect to be
radio-collared? Provide the standard deviation as well.
(d) The biologist gets back from the
helicopter observation expedition, and was asked the question: How
many radio collared grizzly bears did you see? The biologist cannot
remember exactly, so responds " somewhere between 4 and 8
Given this information, what is the probability that the biologist saw 7 radio-collared grizzly bears?