Question

1. The manager of a self-service carwash station found that customers take an average of 8 minutes to wash and dry their cars. Assuming that the self-service times can be modelled by exponential distribution, compute the probability that a customer will require more than 11 minutes to complete the job.

Answer 1

Solution:

Let X be an random variable which represents the time taken by the customers to wash and dry their cars at a self-service carwash station.

Given that, X is a exponentially distributed random variable with mean time of 8 minutes.

We have to obtain P(X > 11 minutes).

The probability density function of a random variable X with mean λ is given as follows:

We have,  λ = 8 minutes

The probability that a customer will require more than 11 minutes to complete the job is 0.2528.

Note: The probability is rounded to 4 decimal places.

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