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Chirag, Master's Degree
Category: Calculus and Above
Satisfied Customers: 11951
Experience:  I have a Master's degree in Engineering and a very wide teaching experience of more than 25 years at various levels.
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# 7. In a forest, the probability that a randomly sampled tree

### Resolved Question:

7. In a forest, the probability that a randomly sampled tree is oak is 0.1, pine 0.3, maple 0.35 and 0.25 is the probability that a randomly sampled tree is of any other type. If 8 trees are sampled randomly from a forest

(Hint: You may also think of the problem as probability of a tree being oak is 0.1 and non-oak is 0.9).

a) (6 pts) What is the probability that 2 of the 8 trees sampled is oak?

P(Y=8)= 8!/(2!(8-2)!(.1)^2(1-.1)^6=.1488
Binomial with n = 8 and p = 0.1

x P( X = x )
1 0.382638
2 0.148803
3 0.033067
4 0.004593
5 0.000408
6 0.000023
7 0.000001
8 0.000000

b) (6 pts) What is the probability that at least one of the 8 trees sampled is either an oak or a pine?

c) (5 pts) Let Y be a random variable denoting the number of maple trees in the sample of 8. What is the expected value of Y (mean value of Y)? If this value is not a whole number, will you round it up to a whole number?

d) (3 pts) What is the standard deviation of Y?
Submitted: 1 year ago.
Category: Calculus and Above
Expert:  Chirag replied 1 year ago.
WELCOME AND THANKS FOR USING JUST ANSWER.

I am working on your question and will post the answer shortly.

Thanks.
Expert:  Chirag replied 1 year ago.

(a) P(x = 2) = 0.1488

(b) P(At least one is Oak or Pine) = 1 - P(None of the trees is either Oak or Pine)

= 1 - [8!/0! (8 - 0)! 0.4^0 0.68]

= 1 - 0.0168

= 0.9832

(c) p = 0.35

Expected value of Y = np = 8 * 0.35 = 2.8

The rounded up answer is 3

(d) Standard deviation of Y = √(np(1 - p))

= √(8 * 0.35 * (1 - 0.35))

= 1.349

I hope that helps. Let me know if you need any clarifications on my answers. I will be happy to provide them. Else, please give a rating for my answer.

Thanks.

Chirag, Master's Degree
Satisfied Customers: 11951
Experience: I have a Master's degree in Engineering and a very wide teaching experience of more than 25 years at various levels.

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