(1 point) 60% of the employees in a specialized department of a large software f

Question

(1 point) 60% of the employees in a specialized department of a large software firm are computer science graduates. A project team is made up of 10 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 10 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 50 such projects running at the same time and each project team consists of 10 employees as described. On how many of the 50 project teams do you expect there to be exactly 3 computer science graduates? Give your answer to 1 decimal place Part e) I meet 30 employees at random. What is the probability that the second employee I meet is the first one who is a computer science graduate? Give your answer to 3 decimal places. Part f) I meet 72 employees at random on a daily basis. What is the mean number of computer science graduates among the 72 that I meet? Give your answer to one decimal place

Explanation / Answer

Here

Pr(Computer science graduates) = 0.6

Team size = 10

The distribution is binomial here where n= 10 , p = 0.6

(a) Pr(all project employees are CS graduates) = 0.610 = 0.006

(b) Pr(x = 3 ; 10 ; 0.6) = 10C3 (0.6)3(0.4)7 = 0.042

(c) Expected computer science graduates in the team = 10 * 0.6 = 6

(d) Here expected number of projects to have exactly 3 computer science graduates = 0.042 * 50 = 2.1

(e) Pr(The second employee i meet is the first one who is a computer science graduate) = Pr(first one is not computer graduate) *Pr(second one is computer graduate) = 0.4 0.6 = 0.24

(f) Mean number of computer science graduates among the 72 that i meet = 72 * 0.6 = 43.2

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