7.2 Exercise ected $7, is o? is , A company manufactures a new type of mosquito repellents with the period of effectiveness that is approximately normally distributed with a th a standard deviation of 30 hours. A sample of 40 repellents was taken and the average period of effectiveness is 290 hours. Calculate a 96% confidence interval for the true mean of the period of effectiveness. Ce 2 A random sample of 100 automobile owners shows that an automobile is driven on average, 23,500 kilometers per year with a standard deviation of 3,900 kilometers. Construct a 99% confidence interval for the average number of kilometers an automobile is driven annually. 3 How large a sample is needed in Question I if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean? 4 An operations manager wants to evaluate the mean time to assemble a product, and it is known that the population standard deviation is 30 seconds. If he wishes to be 95% confident that the sample mean will be within 10 seconds of the population mean. how large should the sample size be? 5 A machine dispenses sugar into 1 kg plastic bags. A sample of nine bags of sugar was taken and the average weight is 1.0056 kg with a standard deviation of 0.0246. Assuming a normal population, determine a 99% confidence interval for the mean weight.schoolchildren. 7 A random sample of 25 bottles of Vitamin C contains, on average, 325.05 mg with a standard deviation of 0.5. Find the 95% confidence interval for the true mean content of this brand of Vitamin C. Assume that the content is normally distributed. 8 Two random samples were taken from two different normal populations. The first sample of size 30 has a mean of 75 and a standard deviation of 5. The second sample of size 40 (taken from the second population) has a mean of 85 with a standard deviation of 7. Construct a 90% confidence interval for M - 2. 9 Two groups of students are being compared on their final examination marks. A random sample of 12 students from the first group has a mean of 85% with a standard deviation of 4%. From the second group, a random sample of 10 students has a mean of 81% with a standard deviation of 5%. Assuming normal populations with equal variances, determine a 90% confidence interval for the difference between the population means. 10 A transportation company is considering whether to purchase type R or type S tires for its fleet of trucks. To evaluate the difference in these two types of tires, the company has conducted a test using 15 tires of each type. Each tire is tested on traveling distance in a controlled environment until it wears out. The results are as follows: Type R: x, = 36,300 km, s, = 5,000 km Type S: X2 = 38,100 km, $2 = 6,100 km Assuming normal populations, construct a 99% confidence interval for / - H2. 11 Two hundred graduating students are selected and it is found that 114 will be awarded the first class honors degrees. Calculate the 96% confidence interval for the proportion of the graduating students who will receive the first class honors degrees. 12 In a random sample of 500 homes in a district, it is found that 125 do not pay rent. Find the 99% confidence interval for the proportion of homes in this district that do not pay rent