Final answer:
To find the probabilities in this question, we need to use the concept of probability and apply it to the given situation. We can use the binomial probability formula to find the probability of getting a certain number of guppies in the sample. We can also calculate the expected number of guppies and the variance of the guppies.
Step-by-step explanation:
To answer this question, we need to use the concept of probability and apply it to the given situation. Let's break down each part of the question:
(a) To find the probability of exactly 4 guppies in the sample, we can use the binomial probability formula. The probability of getting exactly k successes in n trials, where the probability of success is p, is given by:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
In this case, n = 8, k = 4, and p = 0.3. Plugging these values into the formula, we get P(X = 4) = C(8, 4) * 0.3^4 * (1-0.3)^(8-4). Calculate this value to find the probability.
(b) To find the probability of fewer than 2 guppies, we need to find the probabilities of getting 0 guppies and 1 guppy, and then add them together.
(c) To find the probability of exactly 1 non-guppy, we can subtract the probability of getting 0 non-guppies from 1.
(d) To find the expected number of guppies in the sample, we can multiply the probability of getting a guppy by the total number of fish in the sample.
(e) To find the variance of the guppies, we can use the formula: Var(X) = n * p * (1-p), where n is the sample size and p is the probability of success.