Ask Question
9 September, 05:33

The monthly worldwide average number of airplane crashes of commercial airlines is 3.5. What is the probabil - ity that there will be (a) at least 2 such accidents in the next month; (b) at most 1 accident in the next month

+3
Answers (1)
  1. 9 September, 08:51
    0
    Step-by-step explanation:

    We would apply the formula for poisson distribution which is expressed as

    P (x = r) = (e^ - µ * µ^r) / r!

    Where

    µ represents the mean of the theoretical distribution.

    r represents the number of successes of the event.

    From the information given,

    µ = 3.5

    a)

    For the probability that there will be at least 2 such accidents in the next month, it is expressed as

    P (x ≥ 2) = 1 - P (x < 2)

    P (x < 2) = P (x = 0) + P (x = 1)

    Therefore,

    P (x = 0) = (e^ - 3.5 * 3.5^0) / 0!

    P (x = 0) = (e^ - 3.5 * 1) / 1

    P (x = 0) = 0.03

    P (x = 1) = (e^ - 3.5 * 3.5^1) / 1!

    P (x = 1) = (e^ - 3.5 * 3.5) / 1

    P (x = 1) = 0.11

    P (x < 2) = P (x = 0) + P (x = 1) = 0.03 + 0.11 = 0.14

    P (x ≥ 2) = 1 - 0.14 = 0.86

    b)

    For the probability that there will be at most 1 accident in the next month, it is expressed as

    P (x ≤ 1) = P (x = 0) + P (x = 1)

    P (x = 0) = 0.03

    P (x = 1) = 0.11

    P (x ≤ 1) = 0.03 + 0.11 = 0.14
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “The monthly worldwide average number of airplane crashes of commercial airlines is 3.5. What is the probabil - ity that there will be (a) ...” 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