1) 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 figure. (a) What is the minimum UGPA that would still place a student in the top 5% of UGPAs? (b) Between what two values does the middle 50% of the UGPAs lie? A normal curve labeled mu = 3.38 and sigma = 0.21 is over a horizontal x-axis labeled Grade point average from 2.76 to 4 in increments of 0.31 and is centered on 3.38. 2) Find the minimum sample size n needed to estimate for the given values of c, , and E. c=0.98, =6.4, and E=1 Assume that a preliminary sample has at least 30 members. n=.........? (Round up to the nearest whole number.) 3)Find the minimum sample size n needed to estimate for the given values of c, , and E. c=0.98, =7.6, and E=2 Assume that a preliminary sample has at least 30 members. n= .........? (Round up to the nearest whole number.) 4) 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 40 home theater systems has a mean price of $119.00. Assume the population standard deviation is $15.60. Construct a 90% confidence interval for the population mean. The 90% confidence interval is........ , ........? 5) From a random sample of 64 dates, the mean record high daily temperature in a certain city has a mean of 84.54F. Assume the population standard deviation is 14.67F. This creates a 95% confidence interval for the population mean of (80.95, 88.13). Does it seem possible that the population mean could be less than 86F? Explain. Choose the correct answer below. A. Yes, it seems possible because 86F is greater than the right endpoint of the confidence interval. B. No, it does not seem possible because 86F is less than the left endpoint of the confidence interval. C. Yes, it seems possible because 86F is between the endpoints of the confidence interval. D. No, it does not seem possible because 86F is greater than the right endpoint of the confidence interval. 6) A random sample of the closing stock prices in dollars for a company in a recent year is listed below. Assume that is $2.33. Construct the 90% and 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. 20.51 18.36 28.96 17.01 22.44 19.12 16.51 20.32 16.19 18.86 18.14 15.65 18.64 15.39 21.82 21.97 The 90% confidence interval is $.......,$.......? The 99% confidence interval is .......... , .........? 7) A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.15 inch. (a) Determine the minimum sample size required to construct a 99% confidence interval for the population mean. Assume the population standard deviation is 0.6 inch. (b) The sample mean is 26.7 inches. With a sample size of 117, a 99% level of confidence, and a population standard deviation of 0.6 inch, does it seem possible that the population mean could be less than 26.8 inches? Explain. 8) The mean height of women in a country (ages 2029) is 64.3 inches. A random sample of 55 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume =2.63. 9) The weights of ice cream cartons are normally distributed with a mean weight of 12 ounces and a standard deviation of 0.5 ounce. (a) What is the probability that a randomly selected carton has a weight greater than 12.22 ounces? (b) A sample of 25 cartons is randomly selected. What is the probability that their mean weight is greater than 12.22 ounces? 10) Find the probability and interpret the results. If convenient, use technology to find the probability. The population mean annual salary for environmental compliance specialists is about $63,500. A random sample of 35 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $61,000? Assume =$6,200. The probability that the mean salary of the sample is less than $61,000 is ..........?