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- Assume that the readings at freezing on a bundle 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.If 4.1% of the thermometers are rejected because they have readings that are too high and another 4.1% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others.interval of acceptable thermometer readings = _________ °CConsider that μ1 and μ2 are the true mean stopping distances for motorcycles at 30 mph equipped with two different sets of tires. Tire set 1 is more expensive, so we only want to buy them if there is strong evidence that there is a mean stopping distance of at least 3 ft shorter at 30 mph. For Tire set 1, after nine tests, we get an x-bar1 of 110 ft and an s1 of 5 ft. For Tire set 2, after eight tests, we get an x-bar2 of 120 ft and an s2 of 6 ft. Assume that the distributions of stopping distances are roughly normal. (a) Find a point estimate of μ1 – μ2. Is the estimate biased or unbiased? (b) Find the estimated standard error the point estimate of μ1 – μ2? (c) Formulate and test the appropriate hypothesis at the α = 0.05 level.A company claims that the number of defective items manufactured during each run of making 100 of their products is independent of the number from other runs and that the proportion of defectives is not more than 3%. Assuming that the defective rate for each run is 3% Which of the following can be used to determine whether x = 8 is unusually a high number of defective items on the next run of 100 of their products?
- Assume that the readings at freezing on a bundle 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.If 4.8% of the thermometers are rejected because they have readings that are too high and another 4.8% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others.interval of acceptable thermometer readings =_____________ °CThe lifespan of a 100-W fluorescent lamp is define to be normally distributed with σ = 30 hrs. A random sample of 15 lamps has a mean life of x = 1015 hours. Construct a 90% lower-confidence bound on the mean life.Suppose the average size of a new house built in a certain county in 2006 was 2,195 squarefeet. A random sample of 25 new homes built in this county was selected in 2010. Theaverage square footage was 2,272 with a sample standard deviation of 225 square feet. At α =0.025, does this sample provide enough evidence to conclude that the average house size of anew home in the county has increased since 2006? Assume that the house size isapproximately Normal. a. State the null hypothesis and the alternate hypothesis.b. Compute the value of test statistic.c. Draw your conclusion using either the Critical value OR the P-value methodshowing all details
- Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of O°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. If 1.7% of the thermometers are rejected because they have readings that are too high and another 1.7% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others. interval of acceptable thermometer readings = ɔ.The human resources department of a consulting firm gives a standard creativity test to a randomly selected group of new hires every year. This year, 100 new hires took the test and scored a mean of 113.6 points with a standard deviation of 134. Last year, 95 new hires took the test and scored a mean of 116.4 points with a standard deviation of 16.8. Assume that the population standard deviations of the test scores of all new hires in the current year and the test socores of all new hires last year can be estimated by the sample standard deviations, as the samples used were quite large. Construct a 90 confidence interval for the difference between the mean test score , of new hires from the current year and the mean test score , of new hires from last year. Then tind the lower limit and upper limit of the 905% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answeis to at least two decimal places. (If necessary, cosult a list.ot…Suppose that a researcher is interested in estimating the mean systolic blood pressure, μ, of executives of major corporations. He plans to use the blood pressures of a random sample of executives of major corporations to estimate μ. Assuming that the standard deviation of the population of systolic blood pressures of executives of major corporations is 26mm Hg, what is the minimum sample size needed for the researcher to be 95% confident that his estimate is within 5mm Hg of μ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
- Let x be a continuous random variable that is normally distributed with mean u = 30 and standard deviation o = 5. Using the accompanying standard normal distribution table, find P(24 sxs35). E Click the icon to view the standard normal distribution table. The probability is (Round to four decimal places as needed.)Let (X, Y ) be independent and uniformly distributed random variables (RVs) on the interval[0, 1]. Equivalently, let (X, Y ) be a point chosen uniformly at random in the unit box [0, 1] × [0, 1] on the(x, y) plane. Define the RV Z ≜ √X^2−Y^2 as the random distance of the point (X, Y ) from the origin (0, 0). Find the probability density function (PDF) for the RV Z.Suppose that the lifetimes of tires of a certain brand are normally distributed with a mean of 74,500 miles and a standard deviation of o miles. These tires come with a 55,000-mile warranty. The manufacturer of the tires can adjust o during the production process, but the adjustment of o is quite costly. The manufacturer wants to set ở once and for all so that only 1% of the tires will fail before warranty expires. Find the standard deviation to be set. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place. | miles Check esc -> @ 23 24 4. 5 6 1 2 y e tab w/