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 inches too large. clarence's data had a mean of 3.2 inches and a standard deviation pf 0.1 inches. find the mean and standard deviation of the corrected measurements in centimeters. (recall that 1 inch = 2.54 cm)

Question

Mathematics

Aydan Madden

6 April, 15:34

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 inches too large. clarence's data had a mean of 3.2 inches and a standard deviation pf 0.1 inches. find the mean and standard deviation of the corrected measurements in centimeters. (recall that 1 inch = 2.54 cm)

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Aydin · Answer 1

Given that the mean of the over-valued diameters is 3.2 inches.

Given that the measurements are over by 0.2 inches, then the mean of the corrected measurement is given by 3.2 - 0.2 = 3.0 inches.

Thus, the mean of the corrected measurement in centimeters is given by 3.0 x 2.54 = 7.62 centimeters.

Because, the error was done in all the balls, [i. e. each of his measurements is 0.2 inches too large ], the satandard deviation of the corrected measurement will be the same as that of the original measurement.

Therefore, the standard deviation of the corrected measurement is given by 0.1 inches which is equal to 0.1 x 2.54 = 0.254 centimeters.