General hospital admits an average of 10 patients per hour, what is the probability that in the next ½ hour, they will admit 4 patients? A. 0.0189 B. 0.2500 C. 0.7500 D. 0.1755 E. none of the above are correct.
Answers
Step-by-step explanation:
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 !}P(X=k)=
k!
λ
k
×e
−λ
Where, k is number of events expected to observe over time period.
\lambdaλ 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 Here in our problem, λ=8,k=0,e=2.718
\text { Now, } \mathrm{P}(\mathrm{X}=0)=\frac{\mathrm{8}^{0} \times 2.71^{-8}}{0 !} Now, P(X=0)=
0!
8
0
×2.71
−8
=\frac{1 \times 2.71^{-8}}{1}=\frac{1}{2.71^{8}}=0.00033546=
1
1×2.71
−8
=
2.71
8
1
=0.00033546
Hence, the probability of given event is 0.00033546.