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The National Aeronautics and Space Administration (NASA)

Basic Statistics for Business and Economics | 7th Edition | ISBN: 9780077384470 | Authors: Douglas Lind; William Marchal; Samuel Wathen ISBN: 9780077384470 64

Solution for problem 55E Chapter 6

Basic Statistics for Business and Economics | 7th Edition

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Basic Statistics for Business and Economics | 7th Edition | ISBN: 9780077384470 | Authors: Douglas Lind; William Marchal; Samuel Wathen

Basic Statistics for Business and Economics | 7th Edition

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Problem 55E

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?

Step-by-Step Solution:

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.


Step 2 of 1

Chapter 6, Problem 55E is Solved
Textbook: Basic Statistics for Business and Economics
Edition: 7
Author: Douglas Lind; William Marchal; Samuel Wathen
ISBN: 9780077384470

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