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- The scores on a test are normally distributed with a mean of 150 and a standard deviation of 30. Find the score that is 2 1/2 standard deviations above the mean.Define the unit root and cointegration test statistics ?A company makes parts for a machine. The lengths of the parts must be within certain limits or they will be rejected. A large number of parts were measured and the mean and standard deviation were calculated as 3.1 m and 0.005 m respectively. Assuming this data is normally distributed and 99.7% of the parts were accepted, what are the limits?
- The Michelin tires in average will last for 60000 miles. A technician claims that the deviation of mileage for wearied off tires is 25000 miles. If 16 such tires are tested, find the probability that for those tires the average wearied off mileage is between 55000 and 65000 miles.To compare the dry braking distances from 30 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 35 models of Make A and 35 models of Make B. The mean braking distance for Make A is 42 feet. Assume the population standard deviation is 4.7 feet. The mean braking distance for Make B is 45 feet. Assume the population standard deviation is 4.4 feet. At a = 0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles? Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) rari rz (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is/are (Round to three decimal places as needed. Use a comma to separate answers as needed.)It takes an average of 14.5 minutes for blood to begin clotting after an injury. An EMT wants to see if the average will increase if the patient is immediately told the truth about the injury. The EMT randomly selected 70 injured patients to immediately tell the truth about the injury and noticed that they averaged 16.3 minutes for their blood to begin clotting after their injury. Their standard deviation was 4.75 minutes. What can be concluded at the the α = 0.10 level of significance? a. For this study, we should use [Select an answer b. The null and alternative hypotheses would be: Ho: ? Select an answer H₁: ? Select an answer ✓ c. The test statistic ? = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is ? ✓ a f. Based on this, we should [Select an answer the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest the populaton mean is significantly greater than 14.5 at a = 0.10, so…
- A factory manager knows that the pieces produced by their machine will have lengths which are normally distributed, with mean 10 cm and standard deviation 4 mm. If this is true, then 95% of the pieces produced will have lengths between What?The lengths of adult males' hands are normally distributed with mean 187 mm and standard deviation is 7.1 mm. Suppose that 46 individuals are randomly chosen. Round all answers to 4 where possible. Question for the group of 46, find the probability that the average length is more than 188.A soft drink machine can be regulated so it discharges an average of μ oz. per cup. If the ounces of fill are normally distributed, with a standard deviation of 0.4 oz., what value should μ be set at so that 6 oz cups will overflow only 2% of the time?
- e) Suppose that the 3rd quartile is equal to 46. How much data is located above 46? Why?suppose that you work for a government sector for water resources management. Your section is responsible to estimate the required amount of water for household use. Assume that the volume of daily water use per household in North America follows a normal distribution. The mean volume of daily water use is 138 gallons per household and the standard deviation is 46 gallons 1. Sketch the distribution of daily water use (in gallon) per household in North America. Clearly label x and y-axis 2. Find the probability that a randomly selected household in North America uses less than 69 gallons of water per day. Calculate the z-value using the formula and find the probability using the z-table or technologyA water hose manufacturer has developed a light-weight hose for home owners. Besides being constructed of a lightweight material. one of the characteristics of the hose is that it shrinks when it is not in use. When in use, the length of hose extends to its advertised length of 50 feet. Twenty hoses are tested to see if the hoses extend to the length of 50 feet. The sample mean of the length of the hoses is 49 1/2 feet with a s of 15 inches. Test the hypothesis at alpha = .01 that the hoses are not equal to 50 feet.