Question

An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 40, 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

Total number of projects: 25+40=65

(a)

Let X shows the number of projects selected from second section out of 10 graded project. Here X has hypergeometric distribution with parameters

Populaiton size: N= 64

Number of projects from the second section k = 40

Sample size: n=15

The pdf of X is

So the probability that exactly 10 of these are from the second section is

(b)

The probability that at least 10 of these are from the second section is

(c)

The probability that at least 10 of these are from the same section is

(D)

Mean:

Standard deviation:

(e)

Here we have k = 25

Mean:

Standard deviation: