Question

Suppose the time between arrivals of customers at a store closely follows an exponential distribution with a mean of 6.34 minutes.Part A: What is the probability that the arrival of the next customer is less than 3 minutes?Part B: What is the probability that the arrival of the next customer is more than 10 minutes?Part C: Find the probability that the time until the arrival of the next customer is between 5 and 6 minutes.

Answer 1

Answer:

attached below in order

Step-by-step explanation:

Answer 2

The probability that the arrival of the next customer is less than 3 minutes is 0.377, P(X < 10) = 0.206, and P(5< X < 6) = 0.066

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

The time between arrivals of customers at a store closely follows an exponential distribution

Mean = 6.34 minutes

Mean = 1/λ = 6.34

λ = 1/6.34

$\rm P(X < 3) = 1 -e^{-3/3.6}$

P(X < 3) = 0.377

$\rm P(X < 10) = 1 -e^{-10/3.6}$

P(X < 10) = 0.206

$\rm P(5 < X < 6) = e^{-5/3.6}-e^{-6/3.6}$

P(5< X < 6) = 0.066

Thus, the probability that the arrival of the next customer is less than 3 minutes is 0.377, P(X < 10) = 0.206, and P(5< X < 6) = 0.066

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