STAT100 HW#3

Shoshana Levy STAT100 HW #3 1. The following data represent the miles per gallon for a 2013 Ford Fusion for six randomly selected vehicles. Compute the mean and median miles per gallon Data Set: 34.0, 33.2, 37.0, 29.4, 23.6, 25.9 a. Then calculate the sample standard deviation for the data above, show all work Mean: miles/gallon (34. 0 + 33. 2 + 37. 0 + 29. 4 + 23. 6 + 25. 9) /6 = 30. 52 Data in Ascending Order: 23. 6, 25. 9, 29. 4, 33. 2, 34. 0, 37. 0 Middle points average: 39. 4. 6 + 33. 2 / 2 Median = miles/gallon 31. 3 µ = 30. 52 = (23.6−30.52) 2 + (25.9−30.52) 2 + ( 29.4 − 30.52) 2 + ( 33.2−30.52) 2 + (34.0−30.52) 2 + (37.0−30.52) 2 5 Standard Deviation = 5.134 2. The following data represent the amount of time (in min) a random sample of eight students took to complete the online portion of an exam in Sullivan’s Statistics course. Compute the mean and median time Data set: 60.5, 128.0, 84.6, 122.3, 78.9, 94.7, 85.9, 89.9 a. Calculate the sample standard deviation for the above data, show all work Mean: (60. 5 + 128. 0 + 84. 6 + 122. 3 + 78. 9 + 94. 7 + 85. 9 + 89. 9) / 8 = 93. 1 Data in Ascending Order: 60. 5, 78. 9, 84. 6, 85. 9, 89. 9, 94. 7, 122. 3, 128. 0 Middle points average: 85. 9 + 89. 9 / 2 = 87. 9 Median = 87.9 µ = 93. 1 (60.5−93.1) 2 + (128.0−93.1) 2 + (84.6−93.1) 2 + (122.3−93.1) 2 +(78.9−93.1) 2 +(94.7−93.1) 2 +(85.9−93.1) 2 +(89.9−93.1) 2 7 = Standard Deviation = 22.27 3. The weight in grams, of the pairs of kidneys in adult males between the ages of 40 and 49 have a bell shaped distribution with a mean of 325 grams and a standard deviation of 30 grams. Population mean: 325 Population standard deviation: 30 a. About 95% of kidney pairs will be between what weights?

95% 𝑖? 2 ?? ???? ?ℎ? ???? 325 − 2(30) = 265 325 + 2(30) = 385 About 95% will be between 265 and 385 b. What percentage of kidney pairs weighs between 235 grams and 415 grams? 𝑃(235 < 𝑥 < 415) ? = 235−325 30 = − 3 ? = 415−325 30 = 3 So 99.7% of kidney pairs will be between 3 SD of the mean and weight between 235 and 415 grams c. What percentage of kidney pairs weigh less than 235 grams or more than 415 grams? 100 - 99.7% = 0.3% of kidney pairs weigh less than 235 grams or more than 415 grams d. What percentage of kidney pairs weighs between 295 grams and 385 grams? ? = 295−325 30 = − 1 ? = 385 − 325 30 = 2 68% + 13.5% = 81.5% of kidney pairs weight between 295 and 385 grams 4. The distribution of the length of bolts has a bell shape with a mean of 4 inches and a standard deviation of 0.007 inches a. About 68% of bolts manufactured will be between what lengths? 68% 𝑖? 1 ?? ???? ?ℎ? ???? 4 − 0. 007 = 3. 993 4 + 0. 007 = 4. 007 About 68% of bolts will be between 3.993 to 4.007 inches b. What percentage of bolts will be between 3.986 inches and 4.014 inches? ? = 3.986 − 4 0.007 = − 2 ? = 4.014 − 4 0.007 = 2 95% of bolts will be between 2 SD of the mean and weigh between 3.986 and 4.014 inches c. If the company discards any bolts less than 3.986 inches or greater than 4.014 inches, what percentage of bolts manufactured will be discarded? 100% - 95% =5%