<1> Given a random sample as follows: 2, 1, 3, 0, 1, 3, 7, 0, 3, 3, 5, 2, 0, 4, and 2, find the mean, median, mode and sample standard deviation. (2.4, 1.96, 2, 3)
<2> John made 82 in chemistry and 89 in history. The mean grade in chemistry was 68 and the standard deviation was 8, whereas the distribution of history grades had a mean of 80 and a standard deviation of 6. In which class did John score better?(chemistry)
<3> The following scores represent the exam grades for a math course: 50 70 61 91 81 54 62 93 71 71 81 65 56 72 82 96 85 75 68 57 68 75 66 69 76 77 87 77 87 79 . Find the mean and the standard deviation. Find the z-score of 87. Find the interval of 2 standard deviation of the mean. (73.4, 11.5, 1.18, (50.4,96.4))
<4> a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5 ( assuming no replacement )? (100). b) How many of these are odd numbers? (48)
<5> From a group of 5 men and 6 women, how many committees of size 3 are possible: (a) with no restrictions? C(11,3). (b) with 1 man and 2 women? C(5,1)*C(6,2)
<6> A carton of 12 eggs contains 2 spoiled eggs. In how many ways can a person choose 3 eggs and a) get neither of the spoiled eggs? C(10,3). b) get one spoiled egg? C(10,2)*C(2,1)
<7> In how many ways can 3 red, 4 blue and 5 yellow balls be arranged in a straight line? 12!/(3!*4!*5!)
<8> If all the pilots of Lakeville Airlines have been flying an average of 12 years with a standard deviation of 2.7 years, at least what percentage of pilots will have been flying between 8 and 16 years? (54%)
<9> MAT scores for 1000 students were found to have a mean and standard deviation of 550 and 100 respectively. By Chebyshev's Theorem, at least how many of the 1000 scores fall between 350 and 750? (75%)
<10> 3 math books, 2 music books and 4 ecology books are to be arranged on a shelf. None of them are identical. a) How many different permutations are there?( 9!). b) How many permutations are there if books on the same subject are to be grouped together? 1728
<11> a) How many ways can 5 people be lined up to get on a bus? (120). b) If a certain 2 persons insist on following each other, how many ways are possible? (48)
<12> How many different permutations are there of the letters in the word STATISTICS ? (50400)