Question

General hospital has noted that they admit an average of 8 patients per hour. For the last 30 minutes, no patient has been admitted. What is the probability that no patients will be admitted in the next 1 hour?

Answer 1

Answer:0.5

Hope this is correct

Answer 2

ANSWER:

The probability of that no patients will be admitted in the next 1 hour is 0.00033546.

SOLUTION:

Given, General hospital has noted that they admit an average of 8 patients per hour.  

For the last 30 minutes, no patient has been admitted.  

We need to find what is the probability that no patients will be admitted in the next 1 hour?

Let us use the poisson distribution formula for probabilities.

$\mathrm{P}(\mathrm{X}=\mathrm{k})=\frac{\lambda^{k} \times e^{-\lambda}}{k !}$

Where, k is number of events expected to observe over time period.

$\lambda$ is expected value of occurance of event x.

And, "e" is euler’s number.

$\text { Here in our problem, } \lambda=8, \mathrm{k}=0, \mathrm{e}=2.718$

$\text { Now, } \mathrm{P}(\mathrm{X}=0)=\frac{\mathrm{8}^{0} \times 2.71^{-8}}{0 !}$

$=\frac{1 \times 2.71^{-8}}{1}=\frac{1}{2.71^{8}}=0.00033546$

Hence, the probability of given event is 0.00033546.