Question

Clarence measures the diameter of each tennis ball and a bag with a standard ruler. Unfortunately he uses the ruler and correctly so that each of his measurements is 0.2 inches too large. Clarence is data has a mean of 3.2 inches and a standard deviation of 0.1 inches find the mean and standard deviation of the corrected measurements in centimeters

Answer 1

Refer to the figure below.

Assume that there are n correct measurements

`x_(i) , \, i=1,2, \, ... \, n`
Because each measurement has an error of 0.2 in, the actual measurements are

`x_(i) + 2`

From the figure, the analysis indicates that the correct mean is
μ = 3 in = 3*2.54 cm = 7.62 cm
The correct standard deviation is
2.934 in = 2.934*2.54 cm = 7.45 cm


Answer:
μ = 7.62 cm
σ = 7.45 cm