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Answer :
i. The probability that the mean mass of 15 ducks is between 1.15 kg and 1.45 kg can be calculated using the properties of the normal distribution and the given mean and standard deviation.
ii. To find the least value of n such that the probability of the mean mass of a sample being less than 1.4 kg is at least 0.95, we need to determine the sample size that ensures a sufficiently high probability.
iii. The probability that the total mass of 150 ducks is greater than 185 kg can be calculated using the properties of the normal distribution and the given mean and standard deviation, assuming independence of individual duck masses.
i. To calculate the probability that the mean mass of 15 ducks falls between 1.15 kg and 1.45 kg, we can standardize the distribution using the z-score formula and then find the corresponding probabilities using a standard normal distribution table or calculator.
ii. To find the least value of n, we can use the standard normal distribution table or calculator to determine the z-score corresponding to a probability of 0.95. Then, we can solve for n using the formula n = (z * σ / E)^2, where z is the z-score, σ is the standard deviation of the population, and E is the desired margin of error.
iii. To calculate the probability that the total mass of 150 ducks is greater than 185 kg, we can use the properties of the normal distribution and apply the Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases. We assume that individual duck masses are independent.
To know more about standard normal distribution here: brainly.com/question/15103234
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