The number of traffic accidents per day on a certain section of highway is thought to be Poisson distributed with a mean equal 2.19. Based on this, how many traffic accidents should be expected during a week long period?
a. 15.33
b. 10.95
c. approximately 10.36
d. approximately 12.21
e. none of these
If the standard deviation for a Poisson distribution is known to be 3.60, the expected value of that Poisson distribution is:
a. approximately 1.90
b. 3.60
c. 7.2
d. 8.28
e. 12.96
To find the expected number of traffic accidents during a week-long period, we can multiply the mean number of accidents per day by the number of days in a week.
The mean number of traffic accidents per day is given as 2.19.
Number of days in a week = 7
Expected number of traffic accidents during a week-long period = 2.19 * 7 = 15.33
Therefore, the answer is (a) 15.33.
To find the expected value of a Poisson distribution when the standard deviation is known, we can square the standard deviation and then divide it by the mean.
Standard deviation = 3.60
Mean = lambda = ?? (not given)
Since the mean (lambda) is not given, we cannot calculate the expected value.
Therefore, the answer is (e) none of these.
To answer both of these questions, we need to understand the properties of a Poisson distribution and use the mean (μ) and standard deviation (σ) given in each case.
1) To find the expected number of traffic accidents during a week long period, we can use the property of the Poisson distribution that says the mean (μ) is equal to the expected value. So, the expected number of accidents in a week is also equal to the mean.
For the first question, the mean (μ) is given as 2.19. So, we can conclude that the expected number of traffic accidents during a week is 2.19.
Now, let's look at the answer choices and identify the closest option:
a. 15.33
b. 10.95
c. approximately 10.36
d. approximately 12.21
e. none of these
Since the mean is 2.19, none of the given answer choices are close to the expected value. Therefore, the correct answer is e. none of these.
2) To find the expected value of a Poisson distribution when the standard deviation (σ) is known, we can use the formula:
Expected Value = μ = σ^2
For the second question, the given standard deviation (σ) is 3.60. We can use this value to find the expected value:
Expected Value = μ = (3.60)^2 = 12.96
Let's look at the answer choices and identify the closest option:
a. approximately 1.90
b. 3.60
c. 7.2
d. 8.28
e. 12.96
The expected value we calculated is exactly 12.96, so the correct answer is e. 12.96.
The mean is the expected value. An important feature to remember about the Poisson distribution is that the standard deviation is the square root of the mean.
I'll let you take it from here.