(10 points) 70% of the employees in a specialized department of a large software
ID: 3367094 • Letter: #
Question
(10 points) 70% 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 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 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 60 employees at random on a daily basis. What is the mean number of computer science graduates among the 60 that lI meet? Give your answer to one decimal place.Explanation / Answer
Solution:
1. p = 0.7
q = 1 - p = 0.3
a. n=10
P(x=r) = nCr * p^r * q^(n-r)
P(x=10) = 10C10 * 0.7^(10) * 0.3^0 = 0.0282
b. P(x=3) = 10C3 * 0.8^3 * 0.2^7 = 0.009001
c.
x P(x)
0 5.9049E-6
1 1.37781E-4
2 1.4467005E-3
3 0.009001
4 0.036756
5 0.1029193
6 0.200120
7 0.266827
8 0.233474
9 0.121061
10 0.028247
So, 8 number of people in group of 10 is most likely number.
P(x=3) = 0.009001
d. Out of 50 project running,
Number = 50 * 0.009001 = 0.45005
e. if you meet 30 people randomly,
then first one you meet is computer science engineer probability is 0.7 as simple as given in the data.
f. if you meet 60 number of employee daily basis,
number of computer science proffessionals you meet is = 60 * 0.7 = 42
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