A biologist captures 24 grizzly bears during the spring and

A biologist captures 24 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 124 grizzly bears in the population.

(a) What is the probability that of the 15 grizzly bears observed, 3 had radio collars? Use four decimals in your answer.

P(X=3)=

(b) Find the probability that between 3 and 9 (inclusive) of the 15 grizzly bears observed were radio collared?

P(3X9)=

(use four decimals)

(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)=

(use two decimals)

SD(X)=

(use two decimals)

(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 5 and 9 (inclusive) \".

Given this information, what is the probability that the biologist saw 6 radio-collared grizzly bears?

(use four decimals in your answer)

Solution

a) .2496

b) 0.57728

c) E(X)=2.90 var(X)= 2.3413

d) 0.2566