The image features two problem parts related to probability. Here's a detailed transcription suitable for an educational website:---**(c)** Based on your answers to parts **a** and **b**, which value of **p** seems more likely to be true? Explain. *(Enter answer as a division like x/y.)*| P ||---| | | ---**(d)** How small must **p** be made in order to ensure that the probability of no mission failures in 27 attempts is .999? *(Round your answers to 5 decimal places.)* | q | ||---|---|| P | |---**Explanation:** Part (c) asks for a comparison based on previous answers to determine the most likely value of probability **p** and requires an explanation. Part (d) involves calculating a precise probability value to ensure a very high likelihood of zero failures over multiple trials, with the answer rounded to five decimal places. **The January 1986 mission of the Space Shuttle Challenger** was the 25th such shuttle mission. It was unsuccessful due to an explosion caused by an O-ring seal failure.**(a) According to NASA,** the probability of such a failure in a single mission was 1/59,909. Using this value of *p* and assuming all missions are independent, calculate the probability of no mission failures in 27 attempts. Then calculate the probability of at least one mission failure in 27 attempts. *(Do not round your intermediate calculation and round your final answers to 4 decimal places.)*| | ||----------------|--------|| P(x = 0) | || P(x ≥ 1) | |**(b) According to a study conducted for the Air Force,** the probability of such a failure in a single mission was 1/35. Recalculate the probability of no mission failures in 27 attempts and the probability of at least one mission failure in 27 attempts. *(Do not round your intermediate calculation and round your final answers to 4 decimal places.)*| | ||----------------|--------|| P(x = 0) | || P(x ≥ 1) | |

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Description: The image features two problem parts related to probability. Here's a detailed transcription suitable for an educational website:---**(c)** Based on your answers to parts **a** and **b**, which value of **p** seems more likely to be true? Explain. *

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(c) Based on your answers to parts a and b, which value of p seems more likely to be true? Explain. (Enter answer as a division like x/y.) (d) How small must p be made in order to ensure that the probability of no mission failures in 27 attempts is .999? (Round your answers to 5 decimal places.)

(c) Based on your answers to parts a and b, which value of p seems more likely to be true? Explain. (Enter answer as a division like x/y.) (d) How small must p be made in order to ensure that the probability of no mission failures in 27 attempts is .999? (Round your answers to 5 decimal places.)

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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Concept explainers

2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.

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Question

The image features two problem parts related to probability. Here's a detailed transcription suitable for an educational website:

---

**(c)** Based on your answers to parts **a** and **b**, which value of **p** seems more likely to be true? Explain. *(Enter answer as a division like x/y.)*

| P |
|---|
| |

---

**(d)** How small must **p** be made in order to ensure that the probability of no mission failures in 27 attempts is .999? *(Round your answers to 5 decimal places.)*

| q | |
|---|---|
| P | |

---

**Explanation:** Part (c) asks for a comparison based on previous answers to determine the most likely value of probability **p** and requires an explanation. Part (d) involves calculating a precise probability value to ensure a very high likelihood of zero failures over multiple trials, with the answer rounded to five decimal places.

**The January 1986 mission of the Space Shuttle Challenger** was the 25th such shuttle mission. It was unsuccessful due to an explosion caused by an O-ring seal failure.

**(a) According to NASA,** the probability of such a failure in a single mission was 1/59,909. Using this value of *p* and assuming all missions are independent, calculate the probability of no mission failures in 27 attempts. Then calculate the probability of at least one mission failure in 27 attempts. *(Do not round your intermediate calculation and round your final answers to 4 decimal places.)*

| | |
|----------------|--------|
| P(x = 0) | |
| P(x ≥ 1) | |

**(b) According to a study conducted for the Air Force,** the probability of such a failure in a single mission was 1/35. Recalculate the probability of no mission failures in 27 attempts and the probability of at least one mission failure in 27 attempts. *(Do not round your intermediate calculation and round your final answers to 4 decimal places.)*

| | |
|----------------|--------|
| P(x = 0) | |
| P(x ≥ 1) | |

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