1) At a gathering of 195 college students their grade-group and major were recor

Question

1) At a gathering of 195 college students their grade-group and major were recorded as follows: Major Grade-Group A-student B-student C-student Total Biology Nursing Math Accounting Total 25 30 20 75 10 30 10 50 10 10 10 10 30 10 90 50 195 20 40 If a student is selected at random from this group,find the probability that the student is: Question A Biology major A Biology major or an A-student. A Nursing major and a B-student. A Nursing major or a Biology major A math major and a Biology major An Accounting major given that they are anA-student A B-student given that they are a Math major. Answer Points 2) It was discovered that 68% of Yale college students finish their course of study during the required time. In a group of 32 students, find the probability that: Answer Points Question a) 25 students finish their course on time. b) Less than 30 finish their course on time. c) Between 25 and 27 (inclusive) finish on time

Explanation / Answer

1)

1. P( bio mmajor) = (75)/195 = .3846
2. P(a bio or a A-student) = (75+55-25)/195 = .5385
3. P(nursing and B-student) = (50+90-30)/195 = .5641
4. P(math major and bio major) = 0 ( since no student is common between the 2 majors)
5. P( an accounting major given he ' A-student) = 10/40 = .25
6. P( A B-student given he' Math major) = 10/30 = .333

2.

p =.68

n = 32

Mean = np = 32*.68 = 21.76

Stdev = 2.6388

a. P( X=25) = P(Z = (25-21.76)/2.6388 ) = P(Z= 1.23) = 0.218697 = .8903

b. P(X<30) = P(Z< (30-21.76)/2.6388) = P(Z<3.123) = .9991

c. P(25<X<27) = P(Z<(27-21.76)/2.6388)) - P(Z<(25-21.76)/2.6388)  = .9765--.8903 = .0862

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