Assume the random variable x is normally distributed with mean u = 50 and standard deviation 6 = 7. Find the indicated probability. P(x > 40) E> P(x>40)=|:| (Round to four decimal places as needed.) The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution, as shown in the gure. 6' (a) What is the minimum UGPA that would still place a student in the top 10% of UGPAs? 3 30 Q (h) Between what two values does the middle 50% of the UGPAs lie? u ' a 0.1 l3 X 2.6 3.30 4 Grade point average (a) The minimum UGPA that would still place a student in the top 10% of UGPAs is (Round to two decimal places as needed.) (b) The middle 50% of UGPAs lies between on the low end and on the high end. (Round to two decimal places as needed.) You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. A random sample of 60 home theater systems has a mean price of $126.00. Assume the population standard deviation is $19.80. . . . Construct a 90% confidence interval for the population mean. The 90% confidence interval is (,). (Round to two decimal places as needed.) Construct a 95% confidence interval for the population mean. The 95% confidence interval is (,). (Round to two decimal places as needed.) Interpret the results. Choose the correct answer below. O A. With 90% confidence, it can be said that the sample mean price lies in the first interval. With 95% confidence, it can be said that the sample mean price lies in the second interval. The 95% confidence interval is wider than the 90%. O B. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is wider than the 90%. O C. With 90% confidence, it can be said that the population mean price lies in the first interval. With 95% confidence, it can be said that the population mean price lies in the second interval. The 95% confidence interval is narrower than the 90%.Find the margin of error for the given values of c, s, and n. C = 0.90, s = 5, n = 20 - X t-Distribution Table Click the icon to view the t-distribution table. Level of confidence, c 0.80 0.90 0.95 0.98 0.99 One tail, a 0.10 0.05 0.025 0.01 0.005 The margin of error is . (Round to one decimal place as needed.) d.f. Two tails, a 0.20 0.10 0.05 0.02 0.01 d.f. 3.078 6.314 12.706 31.821 63.657 1.886 2.920 4.303 6.965 9.925 N 1.638 2.353 3.182 4.541 5.841 W 1.533 2.132 2.776 3.747 4.604 1.476 2.015 2.571 3.365 4.032 51 0 V a UI A W N 1.440 1.943 2.447 3.143 3.707 1.415 1.895 2.365 2.998 3.499 CO V 1.397 1.860 2.306 2.896 3.355 1.383 1.833 2.262 2.821 3.250 9 1.372 1.812 2.228 2.764 3.169 10 1.363 1.796 2.201 2.718 3.106 11 1.356 1.782 2.179 2.681 3.055 12 1.350 1.771 2.160 2.650 3.012 13 14 1.345 1.761 2.145 2.624 2.977 14 15 1.341 1.753 2.131 2.602 2.947 15 16 1.337 1.746 2.120 2.583 2.921 16 17 1.333 1.740 2.110 2.567 2.898 17 18 1.330 1.734 2.101 2.552 2.878 18 19 1.328 1.729 2.093 2.539 2.861 19 20 1.325 1.725 2.086 2.528 2.845 20 21 1.323 1.721 2.080 2.518 2.831 21 22 1.321 1.717 2.074 2.508 2.819 22 23 1.319 1.714 2.069 2.500 2.807 23 1 218 1 711 2 064 2 402 2 707 24