APU MATH530 Exam 2 Latest 2021 March

MATH530 Applied Statistics

Exam 2

Question 1 It has been observed that electrical connectors manufactured by Jolt Electrical Supply Company last an average of 18.2 months and follow a normal distribution with a standard deviation of 1.7 months. Jolt agrees to replace any connector that fails within 19 months. Out of 500 connectors sold, how many does Jolt expect to replace, on average? Place your answer, rounded to the nearest whole number, in the blank.______

Question 2 The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with mean 6.7 minutes and standard deviation 2.2 minutes. For a door selected at random, what is the probability the assembly line time will be between 5 and 10 minutes? Place your answer, rounded to 4 decimal places, in the blank.______

Question 3 The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound shaped and symmetric with a mean of 25.9 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Place your answer, rounded to 4 decimal places, in the blank.______

Question 4 Political polls typically sample randomly from the U.S population to investigate the percentage of voters who favor some candidate or issue. Suppose that one such poll asks voters how they feel about the President's handling of foreign affairs. The results show that 575 out of the 1280 people polled say they either "approve" or "strongly approve" of the President's handling of foreign affairs. Based on the results of this sample, find a 95% confidence interval estimate for the proportion of the entire voter population who "approve" or "strongly approve" of the President's handling of foreign affairs. Place your answer, rounded to 4 decimal places, in the blanks. Lower limit =___; and upper limit =______

Question 5 Political polls typically sample randomly from the U.S population to investigate the percentage of voters who favor some candidate or issue. Suppose that one such poll asks voters how they feel about the President’s handling of foreign affairs. How large a sample must the pollster take to ensure that, with 95% confidence, he or she could estimate the fraction of voters who “approve” or “strongly approve” of the President’s handling of foreign affairs within 2% of the actual value? Place your answer, rounded to the nearest whole number, in the blank.______

Question 6 The U.S. Department of Transportation requires tire manufacturers to provide tire performance information on the sidewall of the tire so that a prospective customer can be better informed when making a purchasing decision. One very important measure of tire performance is the tread wear index, which indicates the tire's resistance to tread wear compared with a tire graded with a base of 100. This means that a tire with a grade of 200 should last twice as long, on average, as a tire graded with a base of 100. Suppose that a consumer organization wants to estimate the actual tread wear index of a brand name of tires graded 200 that are produced by a certain manufacturer. A random sample of 18 of these tires produced a sample mean tread wear index of 195.3 and a sample standard deviation of 21.4. Assuming that the population of tread wear indices is normally distributed, compute a 95% confidence interval estimate for the population mean tread wear index for tires produced by this manufacturer under this brand name. Place your answer, rounded to 2 decimal places, in the blanks. Lower limit =___; upper limit =___

Question 7 Two growth hormones are being considered. A random sample of 10 rats was given the first hormone and their average weight gain was \f$\bar{x_{1}= 2.3\f$  pounds with standard deviation \f$s_{1} = 0.4\f$  pound. For the second hormone, a random sample of 15 rats had an average weight gain of \f$\bar{x_{2}= 1.9\f$   pounds with standard deviation \f$s_{2} = 0.2\f$  pound. Assume the weight gains follow a normal distribution. Find a 90% confidence interval for the difference in average weight gain for the two growth hormones.

Question options:

0.20 to 0.60 pounds

0.17 to 0.63 pounds

0.15 to 0.65 pounds

0.24 to 0.56 pounds

Question 8 Quality control studies for Dependable Dishwashers show the lifetime of a dishwasher follows a normal distribution with mean \f$\mu  = 8\f$  years and standard deviation \f$\sigma   = 1.2\f$  years. The company will replace any dishwasher that fails during the guarantee period. How long should the company's dishwashers be guaranteed if the company wishes to replace no more than 2% of the dishwashers?

Question options:

0.16 year

0.13 year

5.5 years

10.5 years

Question 9 The manufacturer of a coffee dispensing machine claims that the ounces per cup dispensed is mound shaped and symmetric with mean \f$\mu  = 7\f$  ounces and standard deviation \f$\sigma   = 0.8\f$  ounce. If 40 cups of coffee are measured, what is the probability that the average ounces per cup is between 6.8 and 7.4 ounces?

Question options:

0.0579

0.2902

0.9760

0.9423

Question 10 A random sample of 47 manuscripts typed by Katlyn showed that 13 of them had errors. A random sample of 85 manuscripts typed by Dara showed that 31 of them had errors. Find a 99% confidence interval for the difference in the proportion of all manuscripts with errors typed by Katlyn compared to those typed by Dara.

Question options:

-0.323 to 0.146

-0.252 to 0.076

-0.887 to 0.711

-0.303 to 0.127

Question 11 A manufacturer of computer paper has a production process that operates continuously throughout an entire production shift. The paper is expected to have a mean length of 11 inches and the standard deviation of the length is \f$\sigma  = 0.02\f$  inch. At periodic intervals, a sample is selected to determine whether the mean paper length is still equal to 11 inches or whether something has gone wrong in the production process to change the mean length of the paper produced. You select a random sample of 100 sheets, and the mean paper length is found to be 10.9980 inches. Construct a 95% confidence interval estimate for the population mean paper length. Place your answer, rounded to 4 decimal places, in the blanks.

Question 12 A manufacturing company produces electric insulators. If the insulators break when in use, a short is likely to occur. Thus, destructive testing is carried out to determine how much force is required to break the insulators. Suppose you wish to estimate the mean force required to break the insulators to within \f$\pm 25\f$  pounds with 95% confidence. If on the basis of a study taken the previous year, you believe that the standard deviation is 100 pounds, find the sample size needed. Place your answer, rounded up to the next highest whole number, in the blank.

Question 13 The delivery time for a package sent within the United States is normally distributed with a mean of 4 days and standard deviation of 1 day. If 300 packages are being sent, how many packages do you expect to arrive in less than 3 days? Place your answer, rounded up to the nearest whole number, in the blank.______

Question 14 Maria and Zoe are taking Biology 101 but are in different classes. Maria’s class has an average of 78% with a standard deviation of 5% on the midterm while Zoe’s class has an average of 83% with a standard deviation of 12%. Assume that scores in both classes follow a normal distribution. Now suppose that Maria scored an 84 on the midterm exam and Zoe scored an 89.

Convert Maria’s midterm score of 84 to a standard z-score, rounded to the nearest tenth, and place it in the blank. z-score =

Question 15 Maria and Zoe are taking Biology 101 but are in different classes. Maria’s class has an average of 78% with a standard deviation of 5% on the midterm while Zoe’s class has an average of 83% with a standard deviation of 12%. Assume that scores in both classes follow a normal distribution. Now suppose that Maria scored an 84 on the midterm exam and Zoe scored an 89.

Who did better relative to their class?

Question options:

Maria

Zoe

Cannot Determine

They performed equally

Question 16 Studies have shown that 24% of all students at Richardson High School smoke. Suppose we happen to observe a random sample of 70 Richardson High School students in the school cafeteria. What is the probability that the proportion of those 70 students in the cafeteria who smoke is no more than 20%?

Question options:

0.2600

0.7400

0.5820

0.4180

Question 17 Assuming that weights of newborn babies at a certain hospital are normally distributed with mean 6.5 pounds and standard deviation 1.2 pounds, how many babies in a group of 80 babies from this hospital will weigh more than 8.9 pounds? Place your answer, rounded to the nearest whole number, in the blank.______

Question 18 The diameter of oranges from a Florida orchard are normally distributed with mean \f$\mu  = 3.2\f$  inches and standard deviation \f$\sigma  = 1.1\f$  inches. A packing supplier is designing special occasion presentation boxes for oranges and needs to know the average diameter for a random sample of 8 oranges. If a random sample of 8 oranges is to be taken from this orchard, what is the probability that the mean diameter of these oranges will be smaller than 3 inches? Place your answer, rounded to 4 decimal places, in the blank.

Question 19 A random sample of 56 credit card holders showed that 41 regularly paid their credit card bills on time. Find a 95% confidence interval for p, the proportion of all credit card holders who pay their credit card bills on time. Place your answer, rounded to 4 decimal places, in the blanks. Lower limit =___. Upper limit =______

Question 20 A random sample of 61 students was asked how much they spent for classroom textbooks this semester. The sample standard deviation was found to be s = $28.70. How many more students should be included in the sample to be 99% confident that the sample mean amount spent for textbooks this semester is within $7.00 of the population mean amount spent for textbooks this semester at this college?

Question options:

51

65

38

4