For a weekly town council meeting in a certain town, the distribution of the duration of the meeting is approximately normal with mean 53 minutes and standard deviation 2.5 minutes. For a weekly arts council meeting in the same town, the distribution of the duration of the meeting is approximately normal with mean 56 minutes and standard deviation 5.1 minutes. Let x¯1 represent the average duration, in minutes, of 10 randomly selected town council meetings, and let x¯2 represent the average duration, in minutes, of 10 randomly selected arts council meetings.
Which of the following is the best reason why the sampling distribution of x¯1−x¯2 can be modeled by a normal distribution?
The sample sizes are equal.
Both sample sizes are large enough to satisfy the normality condition.
The population distributions are approximately normal.
The population standard deviations are assumed equal.
The sample sizes are less than 10% of the corresponding population sizes.
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