Question

PROBLEM 1: Engineers redesign fighter aircraft seats to better match women. Before women became combat pilots, the ACES-11 ejector seats were designed for men weighing between 140 pounds and 211 pounds. The population of women has weights distributed normally, with an average of 143 pounds and a standard deviation of 29 pounds. If you select 36 different women at random, calculate the probability that your average sample weight will be between 137 and 139 pounds. POSSIBLE ANSWERS: a) 0.0534 b) 0.0967 c) 0.9033 d) No answer is correct

PROBLEM 2: The following data is about the bending strength (MPa) of concrete beams of a certain type: 5.9, 7.2, 8.3, 6.8, 7.0, 7.3, 8.5, 9.0, 7.2, 6.8, 6.5, 6.0, 7.5, 7.7, 7.9 Calculate the point estimate of the proportion of the beams whose strength to the bending is less than 6.8 MPa POSSIBLE ANSWERS: a) 7.20, the sample median b) 0.8, the sample proportion of beams whose strength is less than 6.8 c) 7.30, the sample mean d) 0.2, the sample proportion of beams whose strength is less than 6.8

PROBLEM 3: The following data is about the bending strength (MPa) of concrete beams of a certain type: 5.9, 7.2, 8.3, 6.8, 7.0, 7.3, 8.5, 9.0, 7.2, 6.8, 6.5, 6.0, 7.5, 7.7, 7.9 Calculate the point estimate of the population standard deviation and say which estimator use POSSIBLE ANSWERS: a) 0.8778, the sample standard deviation b) 7.30, the sample mean c) 109.6, the sum d) 6.80, at sample standard deviation

PROBLEM 4: A taxi company tries to decide whether to buy tires of brand A or B for their taxi fleet. To estimate the difference of the two marks, an experiment is carried out using 12 of each mark. The tires are used until they wear out, resulting in an average of 36,300 kilometers for the brand and 38,100 kilometers for the B brand. Calculate a confidence interval of 90% for the average difference of the two brands, if it is known that the populations are distributed approximately normally with standard deviation of 5000 kilometers for brand A and 6100 kilometers for brand B. POSSIBLE ANSWERS: a) (-5545.129 1945.129) b) (-6545.129 1945.129) c) (-7545.129 1945.129) d) (-5545.129 2945.129)

PROBLEM 5: In a study to compare two different corrosion inhibitors, stainless steel specimens were immersed for four hours in a solution containing sulfuric acid and a corrosion inhibitor. Forty-seven specimens in the presence of inhibitor A had a mean weight loss of 242 mg and a standard deviation of 20 mg, and 42 specimens in the presence of inhibitor B had a mean weight loss of 200 mg. and a standard deviation of 31mg. Determine a 95% confidence interval for the difference in the mean weight loss of the two inhibitors. POSSIBLE ANSWERS: a) (31.01 52.98) b) (30.01 52.98) c) (31.01 53.98) d) (29.01 52.98)

Answer 1