Question

question 5
1 pts
general hospital admits an average of 5 patients per hour. use the poisson probability table below to determine the probability that between 3 and 7 patients (inclusively) are admitted in the next 40 minutes.
poisson probability table with columns for x, 3, 3.333, 5, 7, 7.5, 12 and corresponding probabilities for each x value
options: .5648, .5690, .5044, .0890, .7420, .6263

Explanation:

Step1: Determine the average rate (μ) for 40 minutes

The hospital admits an average of 5 patients per hour. Since 40 minutes is $\frac{40}{60}=\frac{2}{3}$ of an hour, we calculate $\mu$ as $5\times\frac{2}{3}\approx3.333$.

Step2: Find the Poisson probabilities for X = 3, 4, 5, 6, 7

From the Poisson table, for $\mu = 3.333$:

• $P(X = 3)=0.2202$
• $P(X = 4)=0.1835$
• $P(X = 5)=0.1223$
• $P(X = 6)=0.0679$
• $P(X = 7)=0.0324$

Step3: Sum the probabilities

We sum these probabilities: $0.2202 + 0.1835 + 0.1223 + 0.0679 + 0.0324$.
First, $0.2202+0.1835 = 0.4037$; then $0.4037+0.1223 = 0.526$; then $0.526+0.0679 = 0.5939$; then $0.5939+0.0324 = 0.6263$.

Answer:

0.6263