80% of the employees in a specialized department of a large software firm are co

Question

80% of the employees in a specialized department of a large software firm are computer science graduates. A project team is made up of 9 employees. Part a) What is the probability to 3 decimal digits that all the project team members are computer science graduates? Part b) What is the probability to 3 decimal digits that exactly 3 of the project team members are computer science graduates? Part c) What is the most likely number of computer science graduates among the 9 project team members? Your answer should be an integer. If there are two possible answers, please select the smaller of the two integers. Part d) There are 51 such projects running at the same time and each project team consists of 9 employees as described. On how many of the 51 project teams do you expect there to be exactly 3 computer science graduates? Give your answer to 1 decimal place. Part e) I meet 40 employees at random. What is the probability that the fourth employee I meet is the first one who is a computer science graduate? Give your answer to 3 decimal places. Part f) I meet 63 employees at random on a daily basis. What is the mean number of computer science graduates among the 63 that I meet? Give your answer to one decimal place.

Explanation / Answer

Let X denote the actual number of CS graduates

Here, probability value p = 0.80

(a)

P(X=9) = 9C9p9(1-p)9-9 = 1*0.89*0.2(9-9) = 0.134

(b)

P(X=3) = 9C3p3(1-p)9-3 = 84*0.83*0.26 = 0.00275

(c)

E(X) = n*p = 9*0.8 = 7.2

So from the two possible integers 7 and 8, we choose the answer 7

(d)

In this case probability value p = 0.00275 and n = 51

So,

expected number of such projects = n*p = 51*0.00275 = 0.140

Related Questions

Navigate

• Browse (All)
• Browse 8
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.