65% of the employees in a specialized department of a large software firm are co

Question

65% 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. What is the probability to 3 decimal digits that all the project team members are computer science graduates? What is the probability to 3 decimal digits that exactly 3 of the project team members are computer science graduates? 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. There are 42 such projects running at the same time and each project team consists of 10 employees as described. On how many of the 42 project teams do you expect there to be exactly 3 computer science graduates? Give your answer to 1 decimal place I meet 50 employees at random. What is the probability that the third employee I meet is the first one who is a computer science graduate? Give your answer to 3 decimal places. I meet 79 employees at random on a daily basis. What is the mean number of computer science graduates among the 79 that I meet? Give your answer to one decimal place

Explanation / Answer

Part a) Probability that a randomly chosen employee is a computer science graduate is 0.65. As project team is made up of 10 employees, the number of trials is the 10 members of the project, and x, the number of successes, is also 10. So probability = (0.65)^10 = 0.01346274 = 0.013

Part b) We can use the stattrek calculator. Put prob of success as 0.65, no. of trails =10 and no. of successes as 3. Check for binomial prob(X=3). Probability = 0.021

Part c) The expected number of successes in a binomial distribution problem is n * p, or 10 * 0.65, which you would round down to 6.

Part d) Here we can use probability found in b, that a randomly chosen project group has exactly 3 computer science graduates, and use it to get the expected value (mean) of the number of groups with exactly 3 cs grads: P(x=3) * 42 = 0.021 * 42 = 0.882 = 0.9

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