Use the information in Table 1 and the solution to part (a)(iv) to complete the following table, giving your values rounded to three decimal places. Number of failed O-rings 0 1 2 3 4 5 6 Observed proportion
Use the information in Table 1 and the solution to part (a)(iv) to complete the following table, giving your values rounded to three decimal places. Number of failed O-rings 0 1 2 3 4 5 6 Observed proportion
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
-
Use the information in Table 1 and the solution to part (a)(iv) to complete the following table, giving your values rounded to three decimal places.
Number of failed O-rings
0 1 2 3 4 5 6
Observed proportion
Comment briefly on how close the observed proportions of flights
on which 0, 1, 2, . . . , 6 O-ring seals failed are to those predicted by
the binomial model. What does this suggest about the
appropriateness, or otherwise, of the binomial model?
![(a) In 1986, the US Space Shuttle Challenger tragically exploded in flight.
This accident was caused by the catastrophic failure of rubber 'O-ring'
seals that linked segments of the rocket boosters together. There were
six O-ring seals in Challenger (and all other Space Shuttles at the time).
Table 1 shows the numbers of O-ring seal failures that had occurred on
each of 23 previous Space Shuttle flights.
Table 1 Number of O-ring seal failures
Number of failed O-rings
Number of flights
1
2
3
4
5
6
16
0 0
(i) Let p be the probability that an O-ring seal fails on a flight. What
distribution is appropriate to describe the failure or non-failure of a
particular O-ring seal on a particular flight? (Ensure that you
define the corresponding random variable appropriately.)
(ii) A reasonable estimate of p is 3/46 - 0.065. Explain where this
number comes from.
(iii) It is suggested that an appropriate model for the number of O-ring
seals that fail on a particular flight might be a binomial
distribution B(6, p). What assumptions are made by using this
model? In your opinion, is a binomial model appropriate? Briefly
justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f9f9cf9-3921-40f8-9056-55b9c1f47e69%2F18da0402-2d42-4481-a11c-9b345713234a%2Fciv57ir_processed.png&w=3840&q=75)
Transcribed Image Text:(a) In 1986, the US Space Shuttle Challenger tragically exploded in flight.
This accident was caused by the catastrophic failure of rubber 'O-ring'
seals that linked segments of the rocket boosters together. There were
six O-ring seals in Challenger (and all other Space Shuttles at the time).
Table 1 shows the numbers of O-ring seal failures that had occurred on
each of 23 previous Space Shuttle flights.
Table 1 Number of O-ring seal failures
Number of failed O-rings
Number of flights
1
2
3
4
5
6
16
0 0
(i) Let p be the probability that an O-ring seal fails on a flight. What
distribution is appropriate to describe the failure or non-failure of a
particular O-ring seal on a particular flight? (Ensure that you
define the corresponding random variable appropriately.)
(ii) A reasonable estimate of p is 3/46 - 0.065. Explain where this
number comes from.
(iii) It is suggested that an appropriate model for the number of O-ring
seals that fail on a particular flight might be a binomial
distribution B(6, p). What assumptions are made by using this
model? In your opinion, is a binomial model appropriate? Briefly
justify your answer.
![(iv) Use Minitab to obtain a table containing both the p.m.f. and c.d.f.
of the B(6, p) distribution with p = 0.065. (Do not change the
number of decimal places of the values obtained from those
provided by Minitab.)
(v) Use the information in Table 1 and the solution to part (a)(iv) to
complete the following table, giving your values rounded to three
decimal places.
Number of failed O-rings
Observed proportion Probability
1
2
3
4
5
6.
Comment briefly on how close the observed proportions of flights
on which 0, 1,2, . . . , 6 O-ring seals failed are to those predicted by
the binomial model. What does this suggest about the
appropriateness, or otherwise, of the binomial model?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1f9f9cf9-3921-40f8-9056-55b9c1f47e69%2F18da0402-2d42-4481-a11c-9b345713234a%2Fakdfzds_processed.png&w=3840&q=75)
Transcribed Image Text:(iv) Use Minitab to obtain a table containing both the p.m.f. and c.d.f.
of the B(6, p) distribution with p = 0.065. (Do not change the
number of decimal places of the values obtained from those
provided by Minitab.)
(v) Use the information in Table 1 and the solution to part (a)(iv) to
complete the following table, giving your values rounded to three
decimal places.
Number of failed O-rings
Observed proportion Probability
1
2
3
4
5
6.
Comment briefly on how close the observed proportions of flights
on which 0, 1,2, . . . , 6 O-ring seals failed are to those predicted by
the binomial model. What does this suggest about the
appropriateness, or otherwise, of the binomial model?
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