Question

A university found that 20% 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

Answer 1

So, the probability is P=0.2063.

Explanation:

We know that a university found that 20% of its students withdraw without completing the introductory statistics course.

We conclude that p=0.2 and q=1-0.2=0.8.

Assume that 20 students registered for the course.

So, n=20.

We calculate the probability that 2 or fewer will withdraw.

We know that

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

We use the formula

`\boxed{P(X=k)=C_k^n\cdot p^k\cdot q^(n-k)}`

we get:

`P(X=0)=C_0^(20)\cdot 0.2^0\cdot 0.8^(20)\\\\P(X=0)=0.0115\\\\\\P(X=1)=C_1^(20)\cdot 0.2^1\cdot 0.8^(19)\\\\P(X=1)=20\cdot 0.0029\\\\P(X=1)=0.058\\\\\\P(X=2)=C_2^(20)\cdot 0.2^2\cdot 0.8^(18)\\\\P(X=2)=(20!)/(2!(20-2)!)\cdot 0.00072\\\\P(X=2)=190\cdot 0.00072\\\\P(X=2)=0.1368`

Therefore, we get

`P(X\leq 2)=P(X=0)+P(X=1)+P(X=2)\\\\P(X\leq 2)=0.0115+0.058+0.1368\\\\P(X\leq 2)=0.2063\\`

So, the probability is P=0.2063.