Question

Solve problems using Minitab. Show evidence that they used the program by putting screen shots of the results. Will give good rating


2. On a certain cruise, there are, on average, 3 traffic accidents each month. Answer the following:

to. Identify the random process


b. Define a variable


c. Associate the random variable with a distribution and its parameters


Solve the following questions using Minitab:

d. Find the probability that in a period of 2 months exactly 4 accidents will occur

and. Find the probability that at least 20 accidents occur in a period of 6 months

F. Find the probability that in a period of 1 month there will be at most (at most) 9 accidents

Answer 1

2.

On a certain cruise, there are , on average 3 traffic accidents each month

a. Identify the random process.:

This random process is a Poisson random process

b. Define Variable

X : Number of Traffic accidents in a month in a cruise

c.

X follows a Poisson distribution with parameter : (Mean) : 3  and the Probability mass function given by

d.

Find the probability that in a period of 2 months exactly 4 accidents will occur

Given average number of traffic accidents per month = 3

Average number of accidents in two months = 2 x 3=6

X : Number of accidents in 2 months is Poisson distribution with mean = 6

P(X=4)

To solve this minitab;

Select menu item

Calc -> Probability Distribution -> Poisson

After selecting this we get the below screen.

As we need to find the P(X=4) with mean =6;

Select probability radio button . Enter 6 in the mean box and enter 4 in the input constant and press OK

You will get the result in the sessions window.

probability that in a period of 2 months exactly 4 accidents will occur = 0.133853

Probability that at least 20 accidents occur in 6 months

Given average number of traffic accidents per month = 3

Average number of accidents in 6 months =6 x 3=18

X : Number of accidents in 6 months is Poisson distribution with mean = 18

Probability that at least 20 accidents occur in 6 months = P(X20) = 1-P(X<20) = 1-P(X19)

Again

Calc -> Probability Distribution -> Poisson

Since we have to calculate P(X19)

Select Cumulative probability radio button; under average enter 18 and for input constant enter 19 and press OK

In session window the results are displayed.

P(X20) = 1-P(X<20) = 1-P(X19) = 1-0.650916= 0.349084

Probability that at least 20 accidents occur in 6 months = 0.349084

F.

probability that in a period of 1 month there will be at most (at most) 9 accidents

Given average number of traffic accidents per month = 3

X : Number of accidents in 1 months is Poisson distribution with mean = 3

probability that in a period of 1 month there will be at most (at most) 9 accidents = P(X9)

Again

Calc -> Probability Distribution -> Poisson

Since we have to calculate P(X9)

Select Cumulative probability radio button; under average enter 3 and for input constant enter 9 and press OK

And the results are displayed in session window

probability that in a period of 1 month there will be at most (at most) 9 accidents = P(X9) = 0.998898