An instructor who taught two sections of engineering statist

An instructor who taught two sections of engineering statistics last term, the first with 20 students and the second with 30, decided to assign a term project. After all projects had been turned in, the instructor randomly ordered them before grading. Consider the first 15 graded projects.

B) What is the probability that atleast 10 of these are from the second section?

C) What is the probability that 10 of these are from the same section?

D)What are the mean value and standard deviation of the number among these 15 that are from the second section?

Solution

20 students and 30 students in two batches.

From this 15 first graded projects are selected.

B) probability that atleast 10 of these are from the second section

= 20C5 (30C10)+ 20C4(30C11)+20C3(30C12)+...+20C0(30C15)/50C15

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C) probability that 10 of these are from the same section

= (10,5) or (5,10)

= {20C10(30C5)+20C5(30C10)}/50C15

d) If x is the random variable for no of students from Second

x can take 0,1,2,3....15

EAch student is independent and chance for one success = 3/4

Hence mean = np = 30(3/4) = 22.5

Variance = npq = 22.5(0.25) = 5.625

std dev = 2.372