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 :

The probability of success p is given by:

[tex]p=0.39[/tex]

Recall the binomial probability distribution formula:

[tex]Pr(x)=\begin{pmatrix}n \\ x\end{pmatrix}p^x(1-p)^{n-x}[/tex]

The probability of at most 4 is given by:

[tex]Pr(0\leq x\leq4)=P(0)+P(1)+P(2)+P(3)+P(4)[/tex]

The probability Pr(0) is given by:

[tex]Pr(0)=\begin{pmatrix}10 \\ 0\end{pmatrix}0.39^0(1-0.39)^{10-0}=0.0071334291166288[/tex]

Therefore,

[tex]Pr(0\leq x\leq4)=0.65796153140997\approx0.6580[/tex]

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

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