Question

An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 35, 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.

(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 probability that at least 10 of these are from the second section? (Round your answer to four decimal places.)


(c) What is the probability that at least 10 of these are from the same section? (Round your answer to four decimal places.)


(d) What are the mean value and standard deviation of the number among these 15 that are from the second section? (Round your mean to the nearest whole number and your standard deviation to three decimal places.)

mean	projects
standard deviation	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.)

mean	projects
standard deviation	projects

Answer 1

Answer:

Given that:

An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 35, 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.

Students in first section = 25

Students in second section, M = 35

Total students, N = 25+35 = 60

project selected, n = 15

a) What is the probability that exactly 10 of these are from the second section?

P(Exactly 10 from second section) = (35C10 * 25C5) / 60C15

= ((35!/(10!*25!) * (25!/(5!*20!)) / (60!/(15!*45!))

= 0.1834

b) What is the probability that at least 10 of these are from the second section?

P(At least 10 from second section) = P(10) +P(11) +P(12) +P(!3) +P(14) +P(15)

= 0.01834 + 0.0992 + 0.0361 + 0.0083 + 0.0011 +0.0001

= 0.3281

c) What is the probability that at least 10 of these are from the same section?

P(At least 10 from 1st ) = 0.0199 + 0.0044 +0.0006 + 0.0001 + 0.0000 +0.0000

= 0.0250

P(At least 10 from same section) = P(At least 10 from 1st ) + P(At least 10 from 2nd)

= 0.0250 + 0.3281

= 0.3531

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

Mean = (n*M)/N

Mean = (15*35)/60

Mean = 8.75

Standard deviation =

Standard deviation =

Standard deviation =

Standard deviation =

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?

mean = 35 - 8.75 = 26.75

standard deviation = 1.668