Justify your Answers please

Note: Questions #13-#17 are based on the following information: The cholesterol content of large chicken eggs is normally distributed with a mean of 200 milligrams and standard deviation 15 milligrams. 13. What proportion of these eggs have cholesterol content above 205 milligrams? a) 0.2004 b) 0.6293 c) 0.7250 d) 0.3300 e) 0.3707 14. What is the probability that the mean cholesterol content of a random sample of 25 of these eggs is less than 205 milligrams? a) 0.6293 b) 0.9525 () 0.5793 d) 1.67 e) 0.0475 15. In sixty-seven percent of the eggs, the cholesterol content is less than a certain value "C". Find the value of "C" a) 0.33 b) 206.6 c) 210 d) 0.44 e) 193.4 16. To test if the claimed 200 mg value is reasonable, a sample of 60 large eggs is analyzed. Their average cholesterol content is 196 mg. What is the P-value based on this sample? a) 0.0197 b) 0.5239 c) 0.0524 d) 0.0317 e) 0.9803 17. We wish to estimate the cholesterol content in duck eggs. How large a sample should be selected if we can assume that o=15 mg also holds for duck eggs, and we wish our estimate to be correct within 5 mg with 99% confidence? a) 8 b) 99 c) 35 d) 75 e) 6018. The following data lists eight different investment amounts (X) and the amount of interest they earned (Y): X $1000 $2000 $3000 $10000 $500 $5000 $50 $100 $150 $500 $25 $250 What is the best estimate for the regression coefficient r between X and Y? a) r will be positive and close to zero b) r will be positive and close to one c) r will be exactly one d) r will be larger than one e) r will be negative 19. In a study of possible correlation between the height in cm (X) and weight in kg (Y) of chimpanzees, a sample of 40 animals produces a correlation coefficient of r=+0.813 and a regression line with equation Y = 034.X" + 195. What is the expected weight of an 80 cm tall chimpanzee? a) 46.7 kg b) 177.9 kg c) 24.0 kg d) 34.8 kg e) 57.1 kg 20. The following table lists the number of days that five houses had been up for sale, as well as their selling price. X (days) 45 12 3 17 32 Y (10005) 275 401 420 212 365 Calculate the correlation coefficient r between the number of days (X) and the selling price (Y) for this sample. a) - 0.465 b) - 0.219 c) + 0.219 d) + 0.512 e) + 0.897 21. The Vitamin C content of a particular brand of vitamin supplement pills is normally distributed with mean 490 mg and standard deviation 12 mg. What is the probability that a randomly selected pill contains at least 500 mg of Vitamin C? a) 0.7967 b) 0.8333 c) 0.0525 d) 0.1123 e) 0.2033