Question

A petrol pump has two pumps. The service times follow the exponential distribution with mean 4 minutes and cars arrive for service in a poisson process at the rate of 10 cars per hour. Find the probability that a customer has to wait for service. What is the probability that the pumps remain idle?​

Answer 1

Answer:

A petrol pump car arrives in 4 minutes is 1

Answer 2

Answer:

    Probability = 0.66

Explanation:

• The Poisson distribution is a discrete probability function. That means the variable can only take specific values in a given list of numbers, probably infinite.

• For a Poisson distribution, μ is used to denote means/expected value and λ is often used to denote rate parameters. Here the rate parameter is the mean/expected value. Hence we can find that both μ and λ are often used to denote the distribution parameter.

• The expected value of the Poisson distribution is taken as μ.
• μ = $\frac{60}{4}$ = 15 per hour.
• In a poisson process, the average number of successes within a given range is taken as λ.
• λ = 10 per hour
• Probability of customer has to wait for service,

               P (Customer has to wait for service is) = 1 / (μ−λ)

           ⇒ $\frac{1}{15-10}$

           ⇒ 0.2

• Now proportion of time pumps remain idle.
• So, it can be explained by formula λ / μ.
• That is, λ / μ = $\frac{10}{15}$ = 0.66
• Hence, the probability that the pumps remain idle = 0.66

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