An Instructor who taught two sections of e project. After all projects had been

Question

An Instructor who taught two sections of e project. After all projects had been turned In, the Instructor randomly ordered them before grading. Consider the first 15 graded projects. ngineering statistics last term, the first with 25 students and the second with 40, decided to assign a term (a) What Is the probability that exactly 10 of these are from the second section? (Round your answer to four decimal places.) (b) What is the probablity that at least 10 of these are from the second section? (Round your answer to four decimal places.) e) What is the probablity that at leadt 10 of these are from the same section? (Round your answer to four decimal places.) from the second section? (Round your mean to (d) What are the mean value and standard deviation of the number among these 15 that are the nearest whole number and your standard deviation to three decimal places.) projects projects (e) What are the mean value and standard deviation of the number of projects not among these first 15 that are from the second section? (Round your mean to the nearest whole number and your standard deviation to three decimal places.) projects projects

Explanation / Answer

Total student = 25+40 = 65

P [ project is from second section ]= p = 40/65 =  0.6153846

n=15

X= number of projects graded from second section.

X follows binomial distribution.

P[X=x] = nCx px (1-p)n-x

a. P[X=10] = 0.1968588381

b. P[X>=10] = 0.45171134289

c. P [ at lease 10 of them are from same section ] = P[at least 10 of them are from section one]+ P [ at least 10 of them are from second section] = 0.04530185542+0.45171134289 =  0.4970132

d. since X follows binomil distribution.

mean = np

sd= sqrt (np(1-p))

n=15

p=0.6153846

mean = 15*0.6153846= 9.230769

sd = sqrt (15*0.6153846* 0.3846154)

= sqrt (3.550296)

=  1.884223

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