The hourly production of a plastic cup company is tracked over the most recent several months and is found to be normally distributed.Comparing the mean of this data set to a similar data set collected last year during the same months, the business analyst notices that the mean has increased, while the overall shape of the distribution has not.Which of the following would not be a possible explanation for this difference?
A)the overall distribution has shifted to the right
B)one or two large outliers occurred in the more recent data set
C)the mode increased as well
D)one or two small outliers occurred in the earlier data set
E)the overall distribution has shifted to the left

Question

Quizplus · Accepted Answer

The mean of a normally distributed data set increasing while maintaining its overall shape suggests that the entire distribution has shifted to the right (A), not to the left (E). Outliers, whether large (B) or small (D), can affect the mean, but a shift in the mode (C) would also be consistent with the entire distribution moving. Therefore, E is not a possible explanation because it suggests a shift in the opposite direction of the observed increase in the mean.

The Hourly Production of a Plastic Cup Company Is Tracked