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Sagot :
Using the binomial distribution, the probability that:
(a) Exactly 29 of them are spayed or neutered, that is, P(X = 29) = 0.1163.
(b) At most 29 of them are spayed or neutered, that is, P(X ≤ 29) = 0.6648.
(c) At least 28 of them are spayed or neutered, that is, P(X ≥ 28) = 0.5714.
(d) Between 28 and 32 (including 28 and 32) of them are spayed or neutered, that is, P(28 ≤ X ≤ 32) = 0.48345.
A binomial distribution, with a success rate of p on each trial, gives us the probability of x number of success in n number of trials, using the formula:
P(X = x) nCx.pˣ.qⁿ⁻ˣ, where q = 1 - p.
In the question, we are informed that 61% of owned dogs in the United States are spayed or neutered, and are given that 46 owned dogs are randomly selected.
This can be seen as a binomial probability distribution, with n = 46, and p = 61% = 0.61, q = 1 - p = 1 - 0.61 = 0.39.
(a) We are asked for the probability of exactly 29 of them being spayed or neutered.
Thus, x = 29, and we need to find P(X = 29).
Using the given calculator, P(X = 29) = 0.1163.
(b) We are asked for the probability of at most 29 of them being spayed or neutered.
Thus, we need to find P(X ≤ 29).
Using the given calculator, P(X ≤ 29) = 0.6648.
(c) We are asked for the probability of at least 28 of them being spayed or neutered.
Thus, we need to find P(X ≥ 28).
Using the given calculator, P(X ≥ 28) = 0.5714.
(d) We are asked for the probability between 28 and 32 of them are spayed or neutered.
Thus, we need to find P(28 ≤ X ≤ 32), which can be shown as;
P(28 ≤ X ≤ 32) = P(X ≤ 32) - P(X < 28).
Using the given calculator, P(X ≤ 32) = 0.91209.
Using the given calculator, P(X < 28) = 0.42864.
Thus, P(28 ≤ X ≤ 32) = P(X ≤ 32) - P(X < 28) = 0.91209 - 0.42864 = 0.48345.
Thus, using the binomial distribution, the probability that:
(a) Exactly 29 of them are spayed or neutered, that is, P(X = 29) = 0.1163.
(b) At most 29 of them are spayed or neutered, that is, P(X ≤ 29) = 0.6648.
(c) At least 28 of them are spayed or neutered, that is, P(X ≥ 28) = 0.5714.
(d) Between 28 and 32 (including 28 and 32) of them are spayed or neutered, that is, P(28 ≤ X ≤ 32) = 0.48345.
Learn more about the binomial distribution at
https://brainly.com/question/24756209
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