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- A major steel pipeline is used to transport crude oil from an oil production platform to a refinery over a distance of 100 km. Even though the entire pipeline is inspected once a year and repaired as necessary, the steel material is subject to damaging corrosion. Assume that from past inspection records, the mean occurrence rate of corrosion along the pipeline is 0.15/km, what is the probability that there are at least five corrosion sites between inspections? Express your answer in three decimal places.A major steel pipeline is used to transport crude oil from an oil production platform to a refinery over a distance of 100 km. Even though the entire pipeline is inspected once a year and repaired as necessary, the steel material is subject to damaging corrosion. Assume that from past inspection records, the mean occurrence rate of corrosion along the pipeline is 0.15/km, what is the probability that there will be 10 locations of damaging corrosion between inspections? Express your answer in three decimal places.Looking at the ABC company Cat Kibbles data set, the quality manager of that company selects and stores two samples per year from the manufacturing line to do quality checks on. This means that over the period of three years from 2014 to 2016, she selected 6 samples in total, to do testing on. Calculate the probability of a success. Provide this answer to 4 decimal points. Do not use a comma. Use only a period (.) to indicate your decimal
- The mean inside diameter of washers produced by a machine is 0.403 cm and the standarddeviation is 0.005 cm. Washers with an internal diameter less than 0.397 cm or greater than0.406 cm are considered defective. What percentage of the washers produced are defective,assuming the diameters are normally distributed? A pump fails, on the average, once in every 500 hours of operation.(a) Find the probability that the pump has more than one failure during a 500 - hourperiod.(b) What is the probability of exactly 3 failures in 2000 hours of operation?A coin-operated soft-drink machine is designed to discharge, when it isoperating properly, at least 7 ounces of beverage per cup with a standarddeviation of 0.2 ounce. If a random sample of 16 cupful is selected by astatistician for a consumer testing service and the statistician is willing to takea risk of ? = 0.05 of committing a Type I error, compute the power of the testand the probability of a Type II error (?) if the population average amountdispensed is actuallya) 6.9 ounces per cup.b) 6.8 ounces per cupA Food Marketing Institute found that 32% of households spend more than $125 a week on groceries. Assume the population proportion is 0.32 and a simple random sample of 374 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31?Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.
- A Food Marketing Institute found that 26% of households spend more than $125 a week on groceries. Assume the population proportion is 0.26 and a simple random sample of 64 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is between 0.32 and 0.43?Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.Business Weekly conducted a survey of recent graduates from the top MBA programs. On the basis of the survey, assume that 80% of the recent graduates annual salary exceeds $40000. Suppose you take a simple random sample of 84 recent graduates.Note: round all z scores to 2 decimal places and all other numbers to 4 decimal places.Find the probability that less than 90% of the 84 recent graduates have an annual salary exceeding $40000. Beyond representative sampling, what assumptions are needed to satisfy the requirements for this problem? X∼normal or n≥30 X∼normal and n≥30 X∼binomial and at least 5 successes and failures X∼binomial and both np and nq at least 5Business Weekly conducted a survey of recent graduates from the top MBA programs. On the basis of the survey, assume that 65% of the recent graduates annual salary exceeds $75000. Suppose you take a simple random sample of 92 recent graduates.Note: round all z scores to 2 decimal places and all other numbers to 4 decimal places.Find the probability that more than 55% of the 92 recent graduates have an annual salary exceeding $75000. Beyond representative sampling, what assumptions are needed to satisfy the requirements for this problem? X∼normal or n≥30 X∼binomial and both np and nqat least 5 X∼normal and n≥30 X∼binomial and at least 5 successes and failures
- A well-mixed cookie dough will produce cookies with a mean of 7 chocolate chips apiece. What is the probability of getting a cookie with no more than 4 chips? Round to 4 decimal placesThe United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500 of young adults ages 20–39 in the United States. Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals, ?, in Lance's sample who regularly skip breakfast is greater than 122. You may find table of critical values helpful. Express the result as a decimal precise to three places. ?(?>122)= Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 103. Express the result as a decimal precise to three places. ?(?<103)=The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500 of young adults ages 20–39 in the United States. Apply the cnormal to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 122. You may find table of critical values helpful. Express the result as a decimal precise to three places. ?(?>122)= Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 103. Express the result as a decimal precise to three places. ?(?<103)=