Question

(10 points) 80% of the employees in a specialized department of a large software firm are computer science graduates. A project team is made up of 8 employees. Part a) What is the probability to 3 decimal digits that all the project team members are computer science graduates? .168 Part b) What is the probability to 3 decimal digits that exactly 3 of the project team members are computer science graduates? .00918 Part c) What is the most likely number of computer science graduates among the 8 project team members? Your answer should be an integer. If there are two possible answers, please select the smaller of the two integers. 7. Part d) There are 49 such projects running at the same time and each project team consists of 8 employees as described. On how many of the 49 project teams do you expect there to be exactly 3 computer science graduates? Give your answer to 1 decimal place. Part e) I meet 20 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. Part f) I meet 24 employees at random on a daily basis. What is the mean number of computer science graduates among the 24 that I meet? Give your answer to one decimal place.

Could you please show all work for all questions. Thank you!

Answer 1

given

n=8, p=0.8

let X represent the Team members are computer science graduate.

Here X follows the Binomial distribution.

Binomial probability is given by:

P(X = z) = (-)p"(1 – p)-

a.)

P(X = 8) = (*)0.88(1 – 0.8) 8-8 = 0.168 (use excel function := BINOMDI ST(8,8,0.8, FALSE)) b.) P(X = 3) = (3)0.5*(1 – 0.8)823 = 0,009 (use excel function := BINOMDIST(3,8,0.8, FALSE))

c.)

Most likely number = n*p =8*0.8=6.4

Ans: 7

(note: if it does not accept 7, please try with 6 (rounding to lower integer number))

d.)

using probability in (b)

Expected number of group projects = P(x=3) *49=0.009*49=0.441

ans: 0.4

e.)

As we are choosing fist employee, the probability that he is the computer science grad=0.8

f.)

Mean number of computer science graduates among the 24=n*p=24*0.8=19.2