SOLUTION: Question text A wildlife biologist observes four brown bears as they attempt to catch salmon in a river in Alaska. Assume that each bear has a .7 probability of catching a fish a

Click here to see ALL problems on Finance

Question 978036: Question text
A wildlife biologist observes four brown bears as they attempt to catch salmon in a river in Alaska. Assume that each bear has a .7 probability of catching a fish and that the bears fishing attempts are independent. Let the random variable X be the number of bears that catch a fish. Create the probability distribution for X (rounding each to THREE decimal places).
What is the standard deviation of the above distribution? Round to three places.
Answer:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
This is a binomial distribution problem

Use the formula
(n C k)*(p)^(k)*(1-p)^(n-k)
where n = 4, p = 0.7 and k ranges from k = 0 to k = 4

Let's calculate the probabilities

when k = 0, the probability is...
(n C k)*(p)^(k)*(1-p)^(n-k)
(4 C 0)*(0.7)^(0)*(1-0.7)^(4-0)
0.0081
0.008

when k = 1, the probability is...
(n C k)*(p)^(k)*(1-p)^(n-k)
(4 C 1)*(0.7)^(1)*(1-0.7)^(4-1)
0.0756
0.076

when k = 2, the probability is...
(n C k)*(p)^(k)*(1-p)^(n-k)
(4 C 2)*(0.7)^(2)*(1-0.7)^(4-2)
0.2646
0.265

when k = 3, the probability is...
(n C k)*(p)^(k)*(1-p)^(n-k)
(4 C 3)*(0.7)^(3)*(1-0.7)^(4-3)
0.4116
0.412

when k = 4, the probability is...
(n C k)*(p)^(k)*(1-p)^(n-k)
(4 C 4)*(0.7)^(4)*(1-0.7)^(4-4)
0.2401
0.240

Let's wrap all this up into a neat distribution table

k P(X = k)
0 0.008
1 0.076
2 0.265
3 0.412
4 0.240

-------------------------------------------------------------------------------
The standard deviation is equal to

The standard deviation is approximately 0.917