# Mathematics

**Week 4 Quiz**

MATH 533 Applied Managerial Statistics – DeVry

**Question 1: **environmental group at a local college is conducting independent tests to determine the distance a particular make off auto mobile will travel while consuming only one gallon of gas. A sample of five cars is tested and a mean of 28.2 miles is obtained. Assuming that the sample standard deviation is 2.7 miles, find the 95% confidence interval for the mean distance travelled by all such cars using one gallon of gas.

**Question 2:** A random sample of size 30 from a normal population yields = 32.8 with a population standard deviation of 4.51. Construct a 95% confidence interval for ****

**Question 3**: In a manufacturing process a random symbol of 36 bolts manufactured has a mean length of 3 inches with a standard deviation of 0.3 inches. What is the 99% confidence interval for the two mean length of the bolt.

**Question 4: **A federal bank examiner is interested in estimating the mean outstanding defaulted loans balance of all defaulted loans over the last 3 years. A random sample of 20 defaulted loans yield a mean of $67918 with a standard deviation of $16552.40. calculate a 90% confidence interval for the mean balance of defaulted loans over the past 3 years.

**Question 5: **Unoccupied seats on flights cause airline to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. 225 flight records are randomly selected and the number of unoccupied seats is noted with a sample mean of 11.6 seats and a standard deviation of 4.1 seats. How many flights should we select if we wish to estimate m to within 2 seats and be 95% confident.

**Question 6: **A coffee/soup machine at the local bus station is supposed to fill cups with 6 ounces of soup. 10 cups of soup brought with a results of mean of 5.93 ounces and a standard deviation of 0.13 ounces. How large a sample of soups would we need to be 95% confident that the sample mean is within and 0.03 ounces of the population mean?

**Question 7: **Recently, a case of food poisoning was trace to a particular restaurant chain. The source was identified and corrective actions were taken to make sure that the food poisoning would not reoccur. Despite the response of the restaurant chain, many consumers refused to visit the restaurant for sometime after the event. A survey was conducted 3 months after the food poisoning occurred with a sample of 319 patterns connected. Of the 319 contacted, 29 indicated that they would not go back to the restaurant because of the potential of food poisoning. Construct a 95 % confidence interval for the true proportion of the market who still refuse to visit any of the restaurants in the chain 3 months after the event.

**Question 8: **The Ohio department of agriculture tested 203 fuel samples across the state in 1999 for accuracy of the reported octane level. For premium grade, 14 out of 105 samples failed (they did not meet ASPM specification and the FTC octane posting rule). Find a 99% confidence interval for the true population proportion of premium grade fuel quality failures.

**Question 9: **Recently, a case of food poisoning was trace to a particular restaurant chain. The source was identified and corrective actions were taken to make sure that the food poisoning would not reoccur. Despite the response of the restaurant chain, many consumers refused to visit the restaurant for sometime after the event. A survey was conducted 3 months after the food poisoning occurred with a sample of 319 patterns contacted. Of the 319 contacted, 29 indicated that they would not go back to the restaurant because of the potential of food poisoning. What sample size would be needed in order to be 99% confident that the sample proportion is within 0.02 of r, the true proportion of customers who refused to go back to the restaurant.

**Question 10: **The Ohio department of agriculture tested 203 fuel samples across the state in 1999 for accuracy of the reported octane level. For premium grade, 14 out of 105 samples failed (they did not meet ASPM specification and the FTC octane posting rule). How many samples would be needed to create a 99% confidence interval that is within 0.02 of the true proportion of premium grade fuel quality failures.