The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming nothing is known about the shape of the distribution of commuting times, what percentage of these commuting times are between 30 and 110 minutes?Group of answer choicesat least 95%at least 89%at least 0%at least 75%
Question
The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming nothing is known about the shape of the distribution of commuting times, what percentage of these commuting times are between 30 and 110 minutes?Group of answer choicesat least 95%at least 89%at least 0%at least 75%
Solution
To answer this question, we need to use the Empirical Rule, also known as the 68-95-99.7 rule, which applies to a normal distribution. However, the question states that nothing is known about the shape of the distribution of commuting times. Therefore, we cannot apply the Empirical Rule here.
Given this, we cannot definitively determine the percentage of commuting times that are between 30 and 110 minutes. Therefore, the only accurate answer choice is "at least 0%".
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