1) The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution, A normal curve labeled mu = 3.42 and sigma = 0.19 is over a horizontal x-axis labeled Grade point average from 2.84 to 4 in increments of 0.29 and is centered on 3.42. (a) What is the minimum UGPA that would still place a student in the top 15% of UGPAs? (b) Between what two values does the middle 50% of the UGPAs? 2) The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 268 days and a standard deviation of 8 days. (a) What is the minimum pregnancy length that can be in the top 8% of pregnancy lengths? (b) What is the maximum pregnancy length that can be in the bottom 7% of pregnancy lengths? (a) The minimum pregnancy length is nothing days. 3) A water footprint is a measure of the appropriation of fresh water. The per capita water footprint (in mega gallons) in a certain country for a recent year can be approximated by a normal distribution, (a) What water footprint represents the 84th percentile? (b) What water footprint represents the 33rd percentile? (c) What water footprint represents the third quartile? A normal curve labeled mu = 1.59 mega gallons and sigma = 2.89 mega gallons is over a horizontal x-axis labeled Mega gallons from negative 6.41 to 9.59 in increments of 4 and is centered on 1.59. 4) Determine whether you can use the normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use the binomial distribution to find the indicated probabilities. A survey of adults in a region found that 62% have encountered fraudulent charges on their credit cards. You randomly select 100 adults in the region. (a) Find the probability that the number who have encountered fraudulent charges on their credit cards is (a) exactly 66, (b) at least 66, and (c) fewer than 66. 5) A drug tester claims that a drug cures a rare skin disease 80% of the time. The claim is checked by testing the drug on 100 patients. If at least 72 patients are cured, the claim will be accepted. Find the probability that the claim will be rejected assuming that the manufacturer's claim is true. Use the normal distribution to approximate the binomial distribution if possible. 6) Find the margin of error for the given values of c=0.90, =3.7, n=100 LOADING... Click the icon to view a table of common critical values. E=.......? 7) Find the margin of error for the given values of c=0.95, =2.8, n=36 LOADING... Click the icon to view a table of common critical values. E=.........? 8) Construct the confidence interval for the population mean . c=0.90, x=4.4, =0.4, and n=50 A 90% confidence interval for is......., .......? 9) Construct the confidence interval for the population mean . c=0.95, x=16.2, =8.0, and n=40 A 95% confidence interval for is ......., .......? 10) Use the confidence interval to find the margin of error and the sample mean. (0.526,0.630) The margin of error is