**QUESTION**

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.

P(X=4)=

**(b) **Find the probability that between 4
and 9 (inclusive) of the 15 grizzly bears observed were radio
collared?

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.

E(X)=

SD(X)=

**(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
(inclusive) ".

Given this information, what is the probability that the biologist
saw 7 radio-collared grizzly bears?