High School

You have 30 boxes of A1 ball bearings in your plant. You immediately had them weighed. The weights of the boxes are:

40.1, 41.1, 39.5, 40.1, 39.1, 41.2, 37.6, 39.1, 41.6, 40.8, 43.2, 38.9, 38.1, 43.5, 36.9, 39.1, 40.5, 41.2, 37.6, 44.0, 38.0, 39.8, 42.1, 38.6, 41.3, 43.7, 36.9, 43.6, 38.1, 40.2.

Calculate the mean and the standard deviation of this sample.

Options:

A. Mean: 40.1, Standard Deviation: 2.1
B. Mean: 39.9, Standard Deviation: 2.3
C. Mean: 40.0, Standard Deviation: 2.2
D. Mean: 40.2, Standard Deviation: 2.0

Answer :

Final answer:

To calculate the mean and standard deviation of the sample, first, find the mean by summing all weights and dividing by the number of boxes. Next, calculate the standard deviation using the variance formula. The correct values are A) Mean: 40.1 and Standard Deviation: 2.1.

Explanation:

Mean Calculation:

Sum of weights = 40.1 + 41.1 + 39.5 + ... + 38.1 + 40.2 = 1203.4

Mean = Sum of weights / Number of boxes = 1203.4 / 30 = 40.113

Standard Deviation Calculation:

Step 1: Calculate the variance.

Step 2: Standard Deviation = Square root of Variance

After calculations, the Mean is approximately 40.1, and the Standard Deviation is approximately 2.1. Therefore, the correct option is Option A.

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