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.

Total number of projects: 25+35=60

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

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

Population size: N= 60

Number of projects from the second section k = 35

Sample size: n=15

The pdf of X is

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

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

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

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

Since we selecting only 15 projects so either event "at least 10 from first section" or event "at least 10 from second section" can occur. Both events cannot occur simultaneously. If we select at least 10 project from first section than we can select at mos 5 from second section. The probability that at least 10 of these are from the same section is

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

Mean:

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?

Here we have k = 25

Mean:

Standard deviation: