Normal Distribution Probability
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A lawyer commutes daily from his suburban home to his midtown office. On the average the trip one way takes 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of trip times to be normally distributed. What is the probability that a trip will take at least 1/2 hour?
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In this problem, we are looking at a lawyer's commute time, which follows a normal distribution. We want to find the probability that a single trip takes at least half an hour.
Normal Distribution Problem
First, let's identify the given values from the text. The average trip time, or the mean, is twenty-four minutes.
Next, the standard deviation is given as three point eight minutes.
The question asks for the probability that a trip takes at least half an hour. Since our other values are in minutes, let's convert one half hour to thirty minutes.
To find this probability, we first need to convert our value of thirty minutes into a standard z-score.
1. Calculate the Z-score
Plugging in our values, we have thirty minus twenty-four in the numerator, divided by three point eight.
Subtracting twenty-four from thirty gives us six.
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