Question

A university found that 25% of its students withdraw without completing the introductory statistics course. Assume that 30 students registered for the course.Use Microsoft Excel whenever necessary and answer the following questions:Compute the probability that 2 or fewer will withdraw

Answer 1

Answer:

0.0106 = 1.06% probability that 2 or fewer will withdraw

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they withdraw, or they do not. The probability of an student withdrawing is independent of any other student, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

25% of its students withdraw without completing the introductory statistics course.

This means that $p = 0.25$

Assume that 30 students registered for the course.

This means that $n = 30$

Compute the probability that 2 or fewer will withdraw:

This is:

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{30,0}.(0.25)^{0}.(0.75)^{30} = 0.0002$

$P(X = 1) = C_{30,1}.(0.25)^{1}.(0.75)^{29} = 0.0018$

$P(X = 2) = C_{30,2}.(0.25)^{2}.(0.75)^{28} = 0.0086$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0002 + 0.0018 + 0.0086 = 0.0106$

0.0106 = 1.06% probability that 2 or fewer will withdraw