Thank you for visiting A quality assurance analyst is interested in estimating the population mean weight of cat food in boxes for a particular brand The analyst obtains a. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The standard deviation for the weight of cat food in boxes is approximately 193.0 grams.
The Data:
100.1, 100.2, 101.2, 101.3, 10.9, 100.1, 100.1, 100.1, 100.3, 100.3, 100.2, 100.1, 400.0, 405.0, 400.1
Step 1: Calculate the Sample Mean (X)
Mean = (Σ(data points)) / n
Mean = (100.1 + 100.2 + ... + 400.1) / 15
≈ 140.13 grams (rounded to two decimal places).
Step 2: Calculate the Squared Differences (Deviations)
We'll calculate the squared difference for each data point and the mean.
Data Point (x_i) Difference (x_i - Mean) Squared Difference
100.1 -40.03 1602.41
100.2 -39.93 1594.41
101.2 -38.93 1528.41
101.3 -38.83 1513.69
10.9 -129.23 16641.69
100.1 -40.03 1602.41
100.1 -40.03 1602.41
100.1 -40.03 1602.41
100.3 -39.83 1584.49
100.3 -39.83 1584.49
100.2 -39.93 1594.41
100.1 -40.03 1602.41
400.0 259.87 67168.09
405.0 264.87 69852.89
400.1 259.97 67184.09
Step 3: Sum Up the Squared Differences
Σ(Squared Deviation) = sum of all squared deviations calculated in step 2.
The Σ(Squared Deviation) ≈ 382,243.34 grams^2.
Step 4: Calculate Sample Variance (S^2)
Variance = Σ(Squared Deviation) / (n - 1)
Variance = (Σ(Squared Deviation)) / 14
Variance = 382,243.34 grams^2 / 14 ≈ 27,303.09 grams^2 (rounded to two decimal places).
Step 5: Calculate Standard Deviation (S)
Standard Deviation = √(Variance)
Standard Deviation = √(27,303.09 grams^2)
Standard Deviation ≈ 193.0 grams (rounded to one decimal place).
Therefore, the standard deviation for the weight of cat food in boxes is approximately 193.0 grams.
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