(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.

(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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 28%…

A: See the hand written solution

Q: Brandon Mackinnon is considering 3 investment options for his $10,000 savings from working as a…

A: Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of…

A: (a) Let r be the prehistoric artifacts in the 44 liters of sediment. The Poisson distribution would…

Q: Magnetic surveying is one technique used by archaeologists to determine anomalies arising from…

A: Binomial distribution is used to estimate the number of successful trials out of n number of trials…

Q: there is no relationship between age and job satisfaction in hypothesis in a formula form

A: The relationship between two variable is denoted by correlation. Correlation testing is the test of…

Q: Suppose we have a binomial experiment in which success is defined to be a particular quality or…

Q: Based on historical data, your manager believes that 29% of the company's orders come from…

A: From the provided information, Manager believes that 29% of the company's orders come from…

Q: carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train.…

Q: Tire lifetimes: The lifetime of a certain type of automobile tire (in thousands of miles) is…

A: Given: Mean =39 Standard Deviation = 5

Q: The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium…

A: Given,sample size(n)=36mean(μ)=26.75standard deviation(σ)=3.50

Q: (d) P(Z > 2.15) = - i (e) P(-2.34 < Z < 1.76) : =

Q: Suppose X is a binomial random variable with n = 200 and p = 0.4. (Use normal approximation. Round…

Q: Suppose that the number of major defects for each new automobile tests is a random ariable with mean…

A: From the provided information, Mean (µ) = 3.2 Standard deviation (σ) = 2.4 Sample size (n) = 100

Q: You may need to use the appropriate appendix table to answer this question. Given that z is a…

A: P(Z<z)=0.2119Z=-0.80P(-z≤Z≤z)=0.9398P(Z≤z)- P(Z≤-z)=0.9398P(Z≤z)-[1-…

Q: Number of weekly grocery deliveries requested at Wal-Mart is a normal random variable with mean m =…

A: Given: Mean μ=2800 Standard deviation σ=860 Consider X~N2800,8602

Q: (c) Suppose n = 43 and p = 0.20. Can we approximate p by a normal distribution? Why? (Use 2 decimal…

A: From the provided information, n = 43 and p = 0.20

Q: Number of weekly grocery deliveries requested at Wal-Mart is a normal random variable with mean m =…

Q: (c) What is the median failure time of a light bulb? (d) What is the hazard rate?

A: From the above given data the following solution is provided below:

Q: You may need to use the appropriate appendix table to answer this question. Given that z is a…

A: Note:- "Since you have posted a question with multiple sub parts, we will provide the solution only…

Q: of seedlings being approximately three per square yard. If the seedlings are randomly dispersed, the…

Q: of coal into each car. The actual weights of coal loaded into each car are normally distributed,…

Q: The lengths of lumber a machine cuts are normally distributed with a mean of 92 inches and a…

A: (a) Given: μ=92, σ=0.5 The corresponding z-value is calculated as: The probability that the machine…

Q: Assume that the number of new visitors to a website in one hour is distributed as a Poisson random…

Q: In a recent survey, approximately 90% of U.S. adults own a cell phone. Let's assume this can be…

A: Given Information : In a recent study , approximately 90% of US adults own a cell phone . Lets…

Q: True/False: Answer the questions below by selecting "true" or "false". If the answer is false in the…

A: We know that, Discrete random variable: The random variable which gives the values countable and…

Q: per square inch.) (a) At what psi will the TPMS trigger a warning for this car? (Round your answer…

A: Given: data mean = 30psi standard deviation = 2psi

Q: n HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute).…

A: actual mean = 17.2ppm standard deviation = 3.25ppm sample size = 12 The printing speed is actually…

Question

100%

(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 0 1 23 4 5 6
Number of flights
16 5200 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
0
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?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

parts iv and v please

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 27% below the target pressure. Suppose the target tire pressure of a certain car is 31 psi. A. Pressure +31(27% of 31)= When tire pressure is below 22.63, the TPMS triggers a warning for the car. B. Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi. If the car’s average tire pressure is on target, what is the probability that the TPMS will trigger a warning? The probability the TPMS will trigger a warning Prob+P(X<=22.63); =P(X-u/a<=22.63-31/2); =P(z<=-4.185 Norm Distribution); Probability=.00011 C. The manufacturer’s recommended correct inflation range is 29 psi to 33 psi. Assume the tires’ average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire’s inflation is within the recommended range? Probability = ? I'd like to understand how to arrive at the answer. Thank you!
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 28% below the target pressure. Suppose the target tire pressure of a certain car is 28 psi (pounds per square inch.) (a) At what psi will the TPMS trigger a warning for this.car? (Round your answer to 2 decimal place.) When the tire pressure is below 20.16 psi. (b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 3 psi. If the car's average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (Round your answer to 4 decimal places.) Probability .0045 (c) The manufacturer's recommended correct inflation range is 26 psi to 30 psi. Assume the tires' average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire's inflation is within the recommended range? (Round your intermediate calculations and final answer to 4 decimal places.) Probability
Tire lifetimes: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean µ= 39 and standard deviation o = 4. Use the TI-84 Plus calculator to answer the following. (a) What is the probability that a randomly chosen tire has a lifetime greater than 47 thousand miles? (b) What proportion of tires have lifetimes between 35 and 43 thousand miles? (c) What proportion of tires have lifetimes less than 44 thousand miles? Round the answers to at least four decimal places. Part: 0 / 3 Part 1 of 3 The probability that a randomly chosen tire has a lifetime greater than 47 thousand miles is Submit Assignment Next Part © 2021 McGraw-Hill Education. All Rights Reserved. Terms of Use Privacy 85 F ch
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 24% below the target pressure. Suppose the target tire pressure of a certain car is 30 psi (pounds per square inch.) (a) At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) (b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi. If the car’s average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (Round your answer to 4 decimal places.) (c)The manufacturer’s recommended correct inflation range is 28 psi to 32 psi. Assume the tires’ average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire’s inflation is within the recommended range? (Round your intermediate calculations and final answer to 4 decimal places.)
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 88 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean µ = 88 tons and standard deviation o = 0.9 ton. (a) What is the probability that one car chosen at random will have less than 87.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 19 cars chosen at random will have a mean load weight x of less than 87.5 tons of coal? (Round your answer to four decimal places.) (c) Suppose the weight of coal in one car was less than 87.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Yes No Suppose the weight of coal in 19 cars selected at random had an average x of less than 87.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? Yes, the probability that this deviation…
For the last 12 years, Colin has contributed $110 each month into a retirement savings account. If the account earns 7% per year compounded monthly what is the balance of the account at the end of the 12th year?
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure. Suppose the target tire pressure of a certain car is 30 psi (pounds per square inch.) (a) At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) When the tire pressure is below 22.2 .psi. (b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi. If the car’s average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (Round your answer to 4 decimal places.) Probability
How would you solve this?
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 53 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean u = 53 tons and standard deviation o = 1.3 ton. n USE SALT (a) What is the probability that one car chosen at random will have less than 52.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 42 cars chosen at random will have a mean load weight x of less than 52.5 tons of coal? (Round your answer to four decimal places.)
The SAT mathematics scores across the population of high school seniors are a normal random variable with a mean of 500 and a standard deviation of 100. Assume that the SAT mathematics test scores of different students are independent. (a) Find the probability that five randomly chosen seniors all score below 600. (b) What score must a student obtain to be in the 99th percentile?
Let a be a random variable representing the percentage of protein content for early bloom alfalfa hay. The average percentage protein content of such early bloom alfalfa should be u = 17.2%. A farmer's co-op is thinking of buying a large amount of baled hay but suspects that the hay is from a later summer cutting with lower protein content. A small amount of hay was removed from each bale of a random sample of 50 bales. The average protein content from the samples was determined by a local agricultural college to be -15.8% with a sample standard deviation of S = 5.3%- At a = .05, does this hay have lower average protein content than the early bloom alfalfa?
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 70 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean u = 70 tons and standard deviation o = 1.4 ton. n USE SALT (a) What is the probability that one car chosen at random will have less than 69.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 30 cars chosen at random will have a mean load weight x of less than 69.5 tons of coal? (Round your answer to four decimal places.) (c) Suppose the weight of coal in one car was less than 69.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? O Yes O No Suppose the weight of coal in 30 cars selected at random had an average x of less than 69.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? O Yes, the probability that…