A random sample of 25 tablets of buffered aspirin contains, on average, 325.05 mg of aspirin per tablet, with a standard deviation of 0.5 mg. Find the 95% tolerance limits that will contain 90% of the tablet contents for this brand of buffered aspirin. Assume that the aspirin content is normally distributed.
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- A nutritionist claims that the mean tuna consumption by a person is 3.6 pounds per year. A sample of 80 people shows that the mean tuna consumption by a person is 3.5 pounds per year. Assume the population standard deviation is 1.06 pounds. At α=0.08, can you reject the claim?A nutritionist claims that the mean tuna consumption by a person is 3.3 pounds per year. A sample of 70 people shows that the mean tuna consumption by a person is 3.1 pounds per year. Assume the population standard deviation is 1.14 pounds. At α=0.03, can you reject the claim?Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P99, the 99-percentile. This is the temperature reading separating the bottom 99% from the top 1%.
- Assume that the heights of a population of adults form a normal distribution with a mean µ =69 inches and a standard deviation σ =6 inches. A village is known to have tall people. A researcher randomly selects a group of 25 people from this village, and their average height is 5 feet 11 inches. Is the average height of people from this village is different than 69 inches, assuming α=0.05?A certain slope at a ski resort records the time it takes for skiers to ski the entire trail. It finds that the times follow a Normal distribution with a mean of 8.3 minutes and a standard deviation of 2.5 minutes. Let X = the amount of time it takes a randomly selected skier to complete the trail. The owners of the resort decide to use a new groomer on the trail that is supposed to take one minute off skiers' times. Let T = the new times after the grooming. Which of the following is a correct interpretation of the standard deviation of T, the new time to complete this trail? O O T = 1.5; the new time for completing the trail is 1.5 minutes. σT = 2.5; the new time for completing the trail is 2.5 minutes. T = 1.5; the new time for completing the trail will typically vary from the mean by 1.5 minutes. T = 2.5; the new time for completing the trail will typically vary from the mean by 2.5 minutes. T = 3.5; the new time for completing the trail will typically vary from the mean by 3.5…A container of car oil is supposed to contain 1000 milliliters of oil. A quality control manager wants to be sure that the standard deviation of the oil containers is less than 20 milliliters. He randomly selects 10 cans of oil with a mean of 997 milliliters and a standard deviation of 32 milliliters. Test the claim that the standard deviation of the oil containers is greater than 20. Use α = 0.05. Interpret your results.
- Consider a normally distributed population of scores with a mean μ = 100 and σx = 10. What score has a Z value of -0.82?A population of scores has µ=44. In this population, a score of X= 40 corresponds to z= - 0. 50. What is the population standard deviation?A nutritionist claims that the mean tuna consumption by a person is 6 pounds per year. A sample of 80 people shows that the mean tuna consumption by a person is 3.5 pounds per year. Assume the population standard deviation is 1.06 pounds. At α=0.08, can you reject the claim?
- 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 43 feet. Assume the population standard deviation is 4.6 feet. The mean braking distance for Make B is 47 feet. Assume the population standard deviation is 4.2 feet. At α=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) through (e).A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 55 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 57.3 milligrams. Assume the population is normally distributed and the population standard deviation is 7.6 milligrams. Atα=0.07, can you reject the company's claim? Complete parts (a) through (e).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.)