107. A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they' last is approximately normal. Researchers in a hospital used the drug on a random sample of nine patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.7; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4. a. i. 3? : ii. 33 : iii. :1 : iv. :1 1 : b. Define the random variable X in words. c. Define the random variable If in words. d. Which distribution should you use for this problem? Explain your choice. e. Construct a 95% confidence interval for the population mean length of time. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. f. What does it mean to be \"95% confident\" in this problem? 108. Suppose that 14 children, who were learning to ride two-wheel bikes, were surveyed to determine how long they had to use training wheels. It was revealed that they used them an average of six months with a sample standard deviation of three months. Assume that the underlying population distribution is normal. a. Li}: ii. 33: iii.n: iv. n'l : b. Define the random variable X in words. c. Define the random variablef in words. d. Which distribution should you use for this problem? Explain your choice. e. Construct a 99% confidence interval for the population mean length of time using training wheels. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. f. Why would the error bound change if the confidence level were lowered to 90%? 110. Forbes magazine published data on the best small firms in 2012. These were firms that had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. The Table 8.13 shows the ages of the corporate CEOs for a random sample of these firms. 48 58 51 61 56 59 74 63 53 50 59 6O 6O 57 46 55 63 57 47 55 57 43 61 62 49 67 67 55 55 49 Tabb 813 Use this sample data to construct a 90% confidence interval for the mean age of CEO's for these top small firms. Use the Student's t-distribution. 113. Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The grams of fat per serving are as follows: 8; 8; 1D; 7; 9; 9. Assume the underlying distribution is approximately normal. a. Construct a 90% confidence interval for the population mean grams of fat per serving of chocolate chip cookies sold in supermarkets. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. b. If you wanted a smaller error bound while keeping the same level of confidence, what should have been changed in the study before it was done? c. Go to the store and record the grams of fat per serving of six brands of chocolate chip cookies. d. Calculate the mean. e. Is the mean within the interval you calculated in part a? Did you expect it to be? Why or why not