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

Question

3 years ago

10

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?

Mathematics

1 answer:

maw [93] · Answer 1 · 2022-07-01T08:53:51+03:00

maw [93]3 years ago

7 0

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)

P(0<x<5)= e^(-0*2/15)- e^(-5*2/15)=1- e^(-2/3)= approx 0.49