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BigCra
11.03.2020 •
Mathematics
For about $1 billion in new space shuttle expenditures, NASA has proposed to install new heat pumps, power heads, heat exchangers, and combustion chambers. These will lower the mission catastrophe probability to 1 in 120. Assume that these changes are made. Calculate the probability of one or more catastrophes in the next:
(1) two missions
probablility=
(2) five missions
probablility=
(3) ten missions
probablility=
(4) fifty missions
probablility=
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Ответ:
The probability of one or more catastrophes in:
(1) Two mission is 0.0166.
(2) Five mission is 0.0410.
(3) Ten mission is 0.0803.
(4) Fifty mission is 0.3419.
Step-by-step explanation:
Let X = number of catastrophes in the missions.
The probability of a catastrophe in a mission is, P (X) =
.
The random variable X follows a Binomial distribution with parameters n and p.
The probability mass function of X is:
In this case we need to compute the probability of 1 or more than 1 catastrophes in n missions.
Then the value of P (X ≥ 1) is:
P (X ≥ 1) = 1 - P (X < 1)
= 1 - P (X = 0)
(1)
Compute the compute the probability of 1 or more than 1 catastrophes in 2 missions as follows:
(2)
Compute the compute the probability of 1 or more than 1 catastrophes in 5 missions as follows:
(3)
Compute the compute the probability of 1 or more than 1 catastrophes in 10 missions as follows:
(4)
Compute the compute the probability of 1 or more than 1 catastrophes in 50 missions as follows:
Ответ:
7 days
Step-by-step explanation: