A population of adult free-range turkeys has a mean weight of 8.5 kg and a standard deviation of 1.2 kg. A random sample of size 10 is taken from this population. Find the mean and the standard deviation for the total weight of this sample of size 10.
Question
A population of adult free-range turkeys has a mean weight of 8.5 kg and a standard deviation of 1.2 kg. A random sample of size 10 is taken from this population. Find the mean and the standard deviation for the total weight of this sample of size 10.
Solution
The mean and standard deviation of a population are given by the formulas:
Mean = μ = ΣX/N Standard Deviation = σ = sqrt(Σ(X - μ)^2/N)
where:
- ΣX is the sum of all values in the population,
- N is the number of values in the population,
- μ is the mean of the population,
- X is each individual value in the population.
Given that the mean weight (μ) of the turkey population is 8.5 kg and the standard deviation (σ) is 1.2 kg, we can calculate the mean and standard deviation for a sample of size 10.
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Mean of the sample: The mean of the sample is the same as the mean of the population. Therefore, the mean weight of the sample is also 8.5 kg.
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Standard deviation of the sample: The standard deviation of the sample is given by the formula σ_sample = σ/sqrt(n), where n is the sample size. Therefore, the standard deviation of the sample is 1.2 kg/sqrt(10) = 0.379 kg.
Therefore, the mean and standard deviation for the total weight of this sample of size 10 are 8.5 kg and 0.379 kg, respectively.
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