Question

60% 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.

(5 points) 60% of the employees in a specialized department ofa large software fim are computer science graduates A project team is made p of 9 employees Part a) What is the probability to 3 decimal digits that all the project team members are computer sclence graduates? Part b) What Is the probability to 3 decimal digits that exactly 3 of the project team members are computer sclence graduates? Part c) What is the most Ikely number computer sclence 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 55 such projects running at the same time and each project team consists of 9 employees described. On how many of the 55 project teams do you expect there to be exactly 3 computer science graduates? Gve your answer to 1 decimal place Part e)meet 30 emplovees at random, What is the probability that the first emolovee Imeet i the first one who is a computer science graduate? Give your answer to 3 decimal places Part f)I meet employees at random on a daily basis What is the mean number of computer science graduates among the 86 that I meet? Give your answer to one decimal place

Answer 1

a) Number of employees, n = 9

P(computer science graduate), p = 0.6

P(all the project team members are computer science graduates) = 0.6⁹

= 0.010

b) Binomial distribution: P(X) = nCx p^x q^n-x

n = 9

p = 0.6

q = 1-p = 0.4

P(X = 3) = 9C3 x 0.6³ x 0.4⁶

= 0.074

c) Most likely number of computer science graduates in a team of 9 = 9x0.6

= 5

d) Number of teams out of 55 with exactly 3 computer science graduates = 55x0.074

= 4.1

e) P(first employee is the first one who is a computer science graduate) = 0.6

f) Mean number of computer science graduates in 86 = 86x0.6

= 51.6