At an intersection, the red light times are normally distributed with a mean time of 3 minutes and a standard deviation of 0.25
minutes. Approximately what percent of red lights last between 2.5 and 3.5 minutes?
32%
68%
95%
99.7%
32%
68%
95%
99.7%
2 answers:
There are many different ways to solve this. If you are a visual learner, see the image of the normal distribution graph attached. This shows the empirical rule of 68-95-99.7 which means that approximately 68 % of the data is within 1 standard deviation, 95% of the data is within 2 standard deviations, and 99.7 % of the data is within 3 standard deviations.
In this case, the mean is 3 and the since the standard deviation given is 0.25, we are going to have a the center of the graph the number 3 because the mean given is 3 minutes. We move one space to the right and that would represent 3.25 minutes, one more space to the right and that is 3.50 minutes. Similarly, go back to the center of the graph, which we decided would be 3 because it is the mean. Now move one space to the left, this would be 2.75, one more space to the left and this represents 2.50 minutes.
The questions asks to approximately what percent of red lights last between 2.5 and 3.5 minutes. Notice 2.5 and 3.5 fall within 2 standard deviations, and we previously said that 95% of the data is within 2 standard deviations. Therefore, the percent of red lights that last between 2.5 and 3.5 minutes is 95%
In this case, the mean is 3 and the since the standard deviation given is 0.25, we are going to have a the center of the graph the number 3 because the mean given is 3 minutes. We move one space to the right and that would represent 3.25 minutes, one more space to the right and that is 3.50 minutes. Similarly, go back to the center of the graph, which we decided would be 3 because it is the mean. Now move one space to the left, this would be 2.75, one more space to the left and this represents 2.50 minutes.
The questions asks to approximately what percent of red lights last between 2.5 and 3.5 minutes. Notice 2.5 and 3.5 fall within 2 standard deviations, and we previously said that 95% of the data is within 2 standard deviations. Therefore, the percent of red lights that last between 2.5 and 3.5 minutes is 95%
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