Question

If 39% of the people in a community use the emergency room at a hospital in oneyear, find these probabilities for a sample of 10 people. a) At most 4 used the emergency room.b) At least 5 used the emergency room.

Answer 1

The probability of success p is given by:

`p=0.39`

Recall the binomial probability distribution formula:

`Pr(x)=\begin{pmatrix}n \\ x\end{pmatrix}p^x(1-p)^(n-x)`

The probability of at most 4 is given by:

`Pr(0\leq x\leq4)=P(0)+P(1)+P(2)+P(3)+P(4)`

The probability Pr(0) is given by:

`Pr(0)=\begin{pmatrix}10 \\ 0\end{pmatrix}0.39^0(1-0.39)^(10-0)=0.0071334291166288`

Therefore,

`Pr(0\leq x\leq4)=0.65796153140997\approx0.6580`

Therefore the probability of at most 4 is approximately 0.6580

Using a similar procedure, it follows that the probability of at least 5 is approximately 0.3420