Problem 55E

The National Aeronautics and Space Administration (NASA) has experienced two disasters. The Challenger exploded over the Atlantic Ocean in 1986 and the Columbia exploded over East Texas in 2003. There have been a total of 123 space missions. Assume failures continue to occur at the same rate and consider the next 23 missions. What is the probability of exactly two failures? What is the probability of no failures?

Solution :

Step 1 of 1:

We assume failures continue to occur at the same rate and consider the next 23 missions.

So n=23.

The Poisson distribution formula is

P(X=x) =

Where,

is the mean number of occurrences in a particular interval.

e is the constant.

x is the number of occurrences.

P(x) is the probability for a specified the value of x.

Our goal is:

We need to find the probability of exactly two failures and the probability of no failures.

Then the mean of poisson distribution is .

We know that n=23 and is the probability of failure .

= 23

= 23

=

= 0.4070

Then the poisson formula is

P(X=x) =

The probability of exactly two failures is

P(X=2) =

P(X=2) =

P(X=2) =

P(X=2) = 0.0551

Therefore, the probability of exactly two failures is 0.0551.

Then the poisson formula is

P(X=x) =

The probability of no failures is

P(X=0) =

P(X=0) = 0.6656

Therefore, the probability of no failures is 0.6656.