In the literature it is reported that 10% of acorns of a particular oak species
ID: 3377341 • Letter: I
Question
In the literature it is reported that 10% of acorns of a particular oak species have holes due to weevils. An ecologist is trying to explore whether the probability of sampling acorns with holes fits the binomial distribution with p = .1. She (and her ecology class) take 1000 random samples of acorns across a forested region, with each sample consisting of 5 acorns. They then tally the results and find the following results. They also calculate the binomial proportions that they expected.
Categories Number of samples Binomial proportions1
0 damaged acorn 640 .590
1 damaged acorn 250 .328
2 damaged acorns 50 .073
3 damaged acorns 40 .008
4 damaged acorns 18 .00045
5 damaged acorns 2 .00001
1Numbers don’t add up to exactly 1 due to rounding error, but don’t worry about this.
Show calculations of how the number .590 was obtained (in the binomial proportions column).
Explanation / Answer
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 5
p = the probability of a success = 0.1
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.59049 [ANSWER]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.