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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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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  1. 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

Probability

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.
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?
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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