The manager of a gas station has observed that the times required by drivers to fill their car's tank and pay are quite variable. In fact, the times are exponentially distributed with a mean of 7.5 minutes. What is the probability that a car can complete the transaction in less than 5 minutes?

Question

Mathematics

Valeria Dalton

18 December, 12:38

The manager of a gas station has observed that the times required by drivers to fill their car's tank and pay are quite variable. In fact, the times are exponentially distributed with a mean of 7.5 minutes. What is the probability that a car can complete the transaction in less than 5 minutes?

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Answers (1)

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Carter Burton · Answer 1

Answer: 0.49

Step-by-step explanation:

The mean = E[x]=1/l = 7.5 min

l=1/7.5 = 10/75=2/15

The exponential distribution's probability density function is looking like that:

F (x) = l*e^ (-l*x) = 2/15*e^ (-2*x/15)

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