Question

clarence measures the diameter of each tennis ball in a bag with a standard ruler. unfortunately, he uses the ruler incorrectly so that each of his measurements is 0.2 inch too large. clarenees data had a mean of 3.2 inches and a standard deviation of 0.1 inch. (recall that 1 in. = 2.54 cm.)
what is the standard deviation of the corrected measurements in centimeters?
8.128 cm
0.254 cm
25.4 cm
7.62 cm

Explanation:

Step1: Analyze the effect of subtracting a constant on standard deviation

When a constant is subtracted from each data - point (in this case, subtracting \(0.2\) inches to correct the measurement), the standard deviation of the data set in inches does not change. So the standard deviation of the corrected measurements in inches is still \(s = 0.1\) inches.

Step2: Convert the standard deviation from inches to centimeters

We know the conversion factor \(1\) inch \(=2.54\) cm. To convert the standard deviation from inches to centimeters, we use the formula \(s_{cm}=s_{in}\times2.54\).
Substitute \(s_{in}=0.1\) into the formula: \(s_{cm}=0.1\times2.54\).

Answer:

\(0.254\) cm. So the answer is \(0.254\) cm.