Final answer:
The probability that none of the 25 males aged 25 have mass greater than 80kg, given that the probability for one male is 0.16, is approximately 0.023 after using the complement and raising it to the power of 25.
Step-by-step explanation:
The question involves calculating the probability that a sample of individuals will have a characteristic (weight) under a certain value.
Since we are given the probability P(X > 80) = 0.16, we know that the probability of any one individual having a weight of over 80kg is 0.16.
To find the probability that none of the 25 selected males weigh over 80kg, we use the complement of the given probability, which is 1 - P(X > 80) = 1 - 0.16 = 0.84.
This is the probability that one male does not have a mass greater than 80kg. We assume that the selection of individuals is independent.
Therefore, the combined probability for all 25 males is the product of their individual probabilities, which is 0.84^25.
Calculating this, we get: 0.84^25 ≈ 0.023 (rounded to three decimal places), representing the probability that none of the 25 males have mass greater than 80kg.