A coin-operated drink machine was designed to discharge a mean of 8 fluid ounces of coffee per cup. In a test of the machine, the discharge amounts in 22 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 8.11 fluid ounces and 0.19 fluid ounces, respectively. If we assume that the discharge amounts are approximately normally distributed, is there enough evidence, to conclude that the population mean discharge, μ, differs from 8 fluid ounces? Use the 0.05 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H. and the alternative hypothesis H₁. HO (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) H |x D*O S X 020 050 0-0 O

In a large section of a statistics​ class, the points for the final exam are normally​ distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top​ 10% receive​ A's, the next​ 20% received​ B's, the middle​ 40% receive​ C's, the next​ 20% receive​ D's, and the bottom​ 10% receive​ F's. Find the lowest score on the final exam that would qualify a student for an​ A, a​ B, a​ C, and a D. The lowest score that would qualify a student for an A is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a B is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a C is nothing. ​(Round up to the nearest integer as​ needed.) The lowest score that would qualify a student for a D is nothing. ​(Round up to the nearest integer as​ needed.)

Given a normally distributed data set whose mean is 25 standard deviation is 5, what values of x would a z-score of 1.2 have?

The Army reports that the distribution of head circumferences among male soldiers is approximately normal with μ =22.8 inches and σ = 1.1 inches. What is the circumference of a soldier whose head is 2.34 standard deviations above the mean?