Ask Question
22 May, 11:02

The time between calls to a plumbing supply business is exponentially distributed with a mean time between calls of 13 minutes. (a) What is the probability that there are no calls within a 30-minute interval

+1
Answers (1)
  1. 22 May, 13:40
    0
    P (X>30) = 1 - F (30) = 0.0995

    Step-by-step explanation:

    Let X be the exponential distributed random variable of time between the calls with the given mean of 13 minutes

    E (X) = 13

    As we have the continuous random variable (time), the distribution is

    F (x) = 1 - e^ (-λx)

    Now we need to calculate the λ from the formula of exponential distribution which is

    E (X) = 1/λ = 15

    So, λ = 1/15

    Now, we will calculate the probability that there are no call within 30 minutes time interval, It mean we need to find the probability when time is greater than 30 (X>30)

    P (X>30) = 1 - F (30) = 1 - (1 - e^ (-30*1/13)

    P (X>30) = e^ (-30/13) = e^ (-2.3) = 0.0995

    P (X>30) = 0.0995
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “The time between calls to a plumbing supply business is exponentially distributed with a mean time between calls of 13 minutes. (a) What is ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers