Answer:
A university found that 30% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.
a. Compute the probability that 2 or fewer will withdraw (to 4 decimals).
= 0.0355
b. Compute the probability that exactly 4 will withdraw (to 4 decimals).
= 0.1304
c. Compute the probability that more than 3 will withdraw (to 4 decimals).
= 0.8929
d. Compute the expected number of withdrawals.
= 6
Step-by-step explanation:
This is a binomial problem and the formula for binomial is:
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:
Finally, the probability that 2 or fewer students will withdraw is
b) Compute the probability that exactly 4 will withdraw.
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.
E(X) = 3/10 * 20 = 6
Expected number of withdrawals is the 30% of 20 which is 6.