Question

question 1
suppose the average number of occurrences in 3 time periods is 7.2. what would be the value of μ in 4.5 time periods?
10.8
1.875
4.8
5.7
8.7
none of these
question 2
use the poisson probability table below to calculate ( p(x < 5) ) when ( mu = 9 )
(poisson probability table content omitted)
0.0161
0.4261
0.0549
0.0524
0.5904
0.1156

Explanation:

Question 1

Step1: Find the rate per time period

The average number of occurrences in 3 time periods is 7.2, so the rate per time period is $\frac{7.2}{3}=2.4$.

Step2: Calculate μ for 4.5 time periods

Multiply the rate per time period by 4.5: $2.4\times4.5 = 10.8$.

To find $P(X < 5)$ when $\mu = 9$, we need to sum the probabilities for $X = 0, 1, 2, 3, 4$.
From the Poisson table, when $\mu = 9$:

• $P(X = 0)=0.0001$
• $P(X = 1)=0.0011$
• $P(X = 2)=0.0050$
• $P(X = 3)=0.0150$
• $P(X = 4)=0.0337$

Now sum these probabilities: $0.0001 + 0.0011 + 0.0050 + 0.0150 + 0.0337 = 0.0549$.

Answer:

10.8

Question 2