1. A total of 1,300 students have completed the MAT 103 course during the past ten years. A random sample consisting of 25 students who completed the course during the past ten years was selected and their final course grades are summarized in the following table. Assuming the sample group is representative of prior students who have completed MAT 103, and assuming prior students who have completed the course are representative of future students who will take the course, what is the 95% confidence interval estimate for the mean grade for a future student enrolling in the MAT 103 course?
Student No. Course Grade
1 83.17
2 82.31
3 90.18
4 93.63
5 90.14
6 96.06
7 83.75
8 85.17
9 86.67
10 93.81
11 83.11
12 82.16
13 89.48
14 86.76
15 83.76
16 86.89
17 88.57
18 96.93
19 86.48
20 95.82
21 92.32
22 78.7
23 92.67
24 74.56
25 78.48
2. The following table summarizes the grades for ten group projects that were completed by two different groups of high school students. Which group of students exhibits the least degree of central tendency about the mean value for their project grades?
Project No. Group 1 Grades Group 2 Grades
1 96.11 99.22
2 87.65 96.44
3 84.35 73.61
4 92.01 84.32
5 98.69 68.51
6 83.65 95.58
7 78.35 96.97
8 88.89 77.49
9 94.94 89.35
10 77.22 86.99
3. A standard deck of playing cards consists of fifty-two cards. The cards in each deck consist of four suits, namely spades (♠), clubs (♣), diamonds (♦) and hearts (♥). Each suit consists of thirteen cards, namely ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, and 2. In the game of poker, a royal flush consists of the ace, king, queen, jack, and 10 of the same suit (e.g., ace of spades, king of spades, queen of spades, jack of spades and 10 of spades). What is the probability of randomly selecting five cards from a randomly shuffled deck of playing cards that constitute a royal flush, assuming the order in which the cards are selected is not important, the suit is not important, and each card is not placed back in the deck after it is drawn?
4. 50 students enrolled in a college Physics 101 course recently took a mid-term exam. 13 students earned an A, 10 students earned a B, 8 students earned a C, 9 students earned a D and 10 students earned an F on the exam. The students were queried regarding the number of hours they had devoted to studying for the exam. 12 of the students who earned an A, 8 of the students who earned a B, 6 of the students who earned a C, 2 of the students who earned a D, and 1 of the students who earned an F reported that they had devoted more than 8 hours to studying for the exam. The remaining students reported that they had devoted no more than 8 hours to studying for the exam.
a. What is the probability of a randomly selected student having devoted more than 8 hours to studying for the exam?
b. What is the probability of a randomly selected student having earned an A or a B on the exam given they devoted no more than 8 hours to studying for the exam?