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. clarences 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 mean of the corrected measurements in centimeters? 7.928 cm 7.62 cm 3.1 cm 8.128 cm

Explanation:

Step1: Correct the mean in inches

Since each measurement is \(0.2\) inch too large, the corrected mean in inches is \(\mu_{corrected\ inches}=\mu_{original\ inches}- 0.2\). Given \(\mu_{original\ inches}=3.2\) inches, then \(\mu_{corrected\ inches}=3.2 - 0.2=3\) inches.

Step2: Convert inches to centimeters

We know that \(1\) inch \( = 2.54\) cm. To convert the corrected mean from inches to centimeters, we use the conversion formula \(x_{cm}=x_{in}\times2.54\). Substitute \(x_{in} = 3\) into the formula: \(x_{cm}=3\times2.54\).

$$x_{cm}=7.62$$

Answer:

7.62 cm