a car dealer estimates that they sell two cars on average per week. they only have space in their showroom for 4 cars. if stock replacement cannot take place within a week, what is the probability assuming that weekly car sales follow a poisson distribution that, the dealer will run out of stock in any one week?
question 2
the table below presents data relating the number of weeks of experience in a job involving the wiring of maniature electronic components an d the number of components which were rejected during the past week for 12 randomly selected wokers
weeks of experience #of rejects
7 26
9 20
6 28
14 16
8 23
12 18
10 24
4 26
2 38
11 22
1 32
8 25
determine the regression equation for predicting the number of components rejected given the number of weeks experience.
1.2 estimate the number of components rejected for an employee with three weeks experience in the job.
1.23 determine the value of the correlation coeffient and comment on this value
Mary: you have asked a lot of questions. I am reluctant to give you the answers as that would be just doing your homework. So, do some research, then take a shot.
(EXCEL or some other statistical software package is very helpful with these types of problems.)
For #1, use a Poisson distribution formula.
Poisson distribution (m = mean):
P(x) = e^(-m) m^x / x!
For #2, see your previous post on your other regression and correlation problem for some hints on how to do this one (if you need to do this by hand). If not, as others have suggested, you can use easier methods.
For Question 1:
To find the probability that the dealer will run out of stock in any given week, we can use the Poisson distribution formula. The mean, or average, number of cars sold per week is given as 2.
The Poisson distribution formula is:
P(x) = (e^(-m) * m^x) / x!
Where:
- P(x) is the probability of x events occurring,
- m is the average number of events in the given time period,
- e is the base of natural logarithms (approximately 2.71828),
- x is the number of events occurring in the given time period,
- x! represents the factorial of x.
In this case, we want to calculate the probability of running out of stock, which means the dealer sells more than 4 cars in a week. So, we need to calculate the probability of selling 5 or more cars in a week.
P(x >= 5) = 1 - P(x < 5)
= 1 - P(x = 0) - P(x = 1) - P(x = 2) - P(x = 3) - P(x = 4)
Now, we can substitute the values into the Poisson distribution formula to calculate each individual probability and then subtract them from 1.
For Question 2:
To determine the regression equation for predicting the number of components rejected given the number of weeks of experience, you'll need to perform a linear regression analysis. This involves finding the equation of a straight line that best fits the given data points.
There are different methods to perform linear regression, but one common approach is to use the least squares method. This method finds the line that minimizes the sum of the squared distances between the actual data points and the predicted values on the line.
Once you have the regression equation in the form of "y = mx + c" (where y is the number of components rejected and x is the number of weeks of experience), you can use it to predict the number of components rejected for a given number of weeks of experience.
To estimate the number of components rejected for an employee with three weeks of experience in the job, simply substitute x = 3 into the regression equation and solve for y.
For the value of the correlation coefficient, you can calculate it using the formula for the Pearson correlation coefficient (r). This measures the strength and direction of the linear relationship between two variables (in this case, the number of weeks of experience and the number of components rejected).
Once you have calculated the correlation coefficient, you can interpret its value. A correlation coefficient of 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship. Values between -1 and 1 represent the strength and direction of the linear relationship, with values closer to -1 or 1 indicating a stronger relationship.