A researcher records the sound (in decibels)during a series of lessons taught by a substitute teacher at a local elementary school.In his study,he found that the sound was 80±6 (M±SD)decibels.Assuming the data are normally distributed,which of the following is an appropriate conclusion?
A)68% of classes were between 68 and 80 decibels.
B)5% of classes were louder than 68 decibels.
C)95% of classes were between 68 and 92 decibels.
D)all of the above

Question

Quizplus · Accepted Answer

Since the data is normally distributed and the mean (M) is given as 80 and standard deviation (SD) is given as 6, we can use the empirical rule or the 68-95-99.7 rule to answer the question.

According to the 68-95-99.7 rule, approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within 2 standard deviations of the mean, and 99.7% of the data falls within 3 standard deviations of the mean.

Therefore, we can conclude that 95% of the classes were between 68 and 92 decibels, which corresponds to 2 standard deviations from the mean. Option C is the only one that correctly represents this conclusion. Option A is incorrect because it only represents 1 standard deviation from the mean, and option B is incorrect because it does not take into account the standard deviation of the data.

A Researcher Records the Sound (In Decibels)during a Series of Lessons