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Answer:
The probability it will take a resident of the city between 17.24 and 42.13 minutes to travel to work is 0.3046.
Step-by-step explanation:
The random variable <em>X</em> can be defined as the travel times to get to work.
The expected travel time is, <em>μ</em> = 38.3 minutes.
The distribution of random variable <em>X</em> can be defined as the distribution of time interval between which a person reaches their work place at a constant average rate.
This implies that <em>X</em> follows an Exponential distribution with parameter, .
The probability density function of <em>X</em> is:
Compute the probability it will take a resident of the city between 17.24 and 42.13 minutes to travel to work as follows:
Thus, the probability it will take a resident of the city between 17.24 and 42.13 minutes to travel to work is 0.3046.