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 8 minutes. What is the probability that a car can complete the transaction in less than 5 minutes

The probability that a car driver can complete the transaction in less than 5 minutes is 0.4647.

Step-by-step explanation:

Let X = times required by drivers to fill their car's tank and pay.

The average time required by drivers is, β = 8 minutes.

The random variable X is Exponentially distributed with parameter, .

The probability distribution function of exponential distribution is:

Compute the probability that a car driver can complete the transaction in less than 5 minutes as follows:

Thus, the probability that a car driver can complete the transaction in less than 5 minutes is 0.4647.

need more info

step-by-step explanation:

-7/8

step-by-step explanation:

instead of subtracting you add the -6/8 and -1/8