Auniversity found that 30% of its students withdraw without completing the introductory statistics course. assume that 20 students registered for the course. compute the probability that 2 or fewer will withdraw (to 4 decimals). compute the probability that exactly 4 will withdraw (to 4 decimals). compute the probability that more than 3 will withdraw (to 4 decimals). compute the expected number of withdrawals.

Step-by-step explanation:

a) Compute the probability that 2 or fewer will withdraw

First we need to determine, given 2 students from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by:

.

Then, we must multiply this quantity by

which is the number of ways to choose 2 students from the total of 20. Therefore:

Following an analogous process we can determine that:

Finally, the probability that 2 or fewer students will withdraw is

b) Compute the probability that exactly 4 will withdraw.

Following the process explained in a), the probability that 4 student withdraw is given by

c) Compute the probability that more than 3 will withdraw

First we will compute the probability that exactly 3 students withdraw, which is given by

Then, using a) we have that the probability that 3 or fewer students withdraw is 0.0355+0.0716=0.1071. Therefore the probability that more than 3 will withdraw is 1-0.1071=0.8929

d) Compute the expected number of withdrawals.

As stated in the problem, 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.

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