A sample of recorded dog barks is analyzed for decibel intensity.The mean intensity is 62.25 decibels, with a variance of 4.45.If this data set is normally distributed, we would expect approximately 95% of the barks to be within what range?
A) (58.03, 66.47)
B) (60.16, 64.36)
C) (55.92, 66.47)
D) (53.35, 71.15)

Question

Quizplus · Accepted Answer

For a normally distributed data set, approximately 95% of the data falls within 2 standard deviations of the mean. The standard deviation is the square root of the variance, which is sqrt(4.45) ≈ 2.11. Therefore, 2 standard deviations is 2 * 2.11 = 4.22. Adding and subtracting this from the mean (62.25 ± 4.22) gives us the range (58.03, 66.47).

A Sample of Recorded Dog Barks Is Analyzed for Decibel