Question

Question 1 - Distribution

The teaching team of ACM is needed to make 4 questions each week for the next week’s lab. The questions created in a week have a Poisson distribution and mean 6

Q 1a)

What is the probability that the teachers manage to write enough questions for the week?

Q 1b)

As some teachers in the team are responsible for other units from ACM, every week, there is a probability of 40% that only half of the them are going to work on the questions. If that is the case, the team creates 3 questions on average. If the fails to finish 4 questions 1 week, what is the probability that only half of the them works that week?

Q 1c)

On week 22, the teachers decides to no longer limit to 4 questions, and instead use every question they make. If a student has a 40% chance of correctly answering questions, and this student is expected to answer 2 questions correctly in the coming lab, what is the probability that the whole team worked on creating the questions that week?

Answer 1

a)

Mean/Expected number of events of interest: λ =                6

P(X=x) = e-λλx/x!

X	P(X)
0	0.0025
1	0.0149
2	0.0446
3	0.0892

P = 1- 0.1512
= 0.8488

b)

X	P(X)
0	0.0498
1	0.1494
2	0.2240
3	0.2240

P(Fail |half work) =0.6472
P(half work) = 0.4

P(fail) = 0.6 *0.1512 + 0.4 * 0.6472

=0.3496

P(half work |Fail) = P(Fail |half work) * P(half work) / P(fail)

= 0.6472*0.4/0.3496

= 0.7405

Thanks in advance!

revert back for doubt

Please upvote