Farmer Max, sells grain to Germany, owns 60 acres of wheat fields. Based on the past experience, he knows that the yield from each individual acre is normally distributed with mean 120 bushels and standard deviation 12 bushels. Help Farmer Max plan for his next year crop by finding:
a) the expected mean of the yields from Farmer Max's 60 acres of wheat
b) the standard deviation of the sample mean of the yields from Farmer Max's 60 acres
a) 120 * 60 = ?
b) Standard Error of the mean (SEm) = SD√n
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To find the expected mean of the yields from Farmer Max's 60 acres of wheat:
Step 1: Calculate the mean yield from each individual acre.
Given the mean μ = 120 bushels.
Step 2: Calculate the total mean yield from 60 acres.
Since each acre has the same mean yield, the total mean yield will be the same as the mean of each individual acre.
Therefore, the expected mean of the yields from Farmer Max's 60 acres of wheat is 120 bushels.
To find the standard deviation of the sample mean of the yields from Farmer Max's 60 acres:
Step 1: Calculate the standard deviation of each individual acre.
Given the standard deviation σ = 12 bushels.
Step 2: Calculate the standard deviation of the sample mean.
The standard deviation of the sample mean, also known as the standard error, is calculated by dividing the standard deviation of the population (σ) by the square root of the sample size (n). In this case, the sample size is 60 (number of acres).
Therefore, the standard deviation of the sample mean is σ/√n = 12/√60 ≈ 1.549 bushels.
So, the standard deviation of the sample mean of the yields from Farmer Max's 60 acres of wheat is approximately 1.549 bushels.
To find the expected mean of the yields from Farmer Max's 60 acres of wheat, you need to multiply the mean yield per acre by the number of acres.
a) The expected mean of the yields from Farmer Max's 60 acres of wheat is calculated as follows:
Expected mean = Mean yield per acre * Number of acres
Expected mean = 120 bushels/acre * 60 acres
Expected mean = 7200 bushels
Therefore, the expected mean yield from Farmer Max's 60 acres of wheat is 7200 bushels.
To find the standard deviation of the sample mean of the yields from Farmer Max's 60 acres, you need to use the formula for the standard deviation of a sample mean.
b) The formula for the standard deviation of a sample mean is given by:
Standard deviation of sample mean = Standard deviation / √(Number of samples)
In this case, the standard deviation is given as 12 bushels and the number of samples is 60 acres. Plugging in these values into the formula, we have:
Standard deviation of sample mean = 12 bushels / √(60 acres)
Standard deviation of sample mean ≈ 1.549 bushels
Therefore, the standard deviation of the sample mean of the yields from Farmer Max's 60 acres is approximately 1.549 bushels.