(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.

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

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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…