A fertilizer manufacturing company buys certain raw materials by weight. EAch batch of raw materials purchaes is weighed and the weigh is recorded to the nearest pound. It is assumed that the round-off- error is uniformly distributed in the interval from -0.7 to +0.7
1. Calculate the mean
2.Calculate the standard deviation
3.Draw the uniform graph
Go to the page below these answers here, where it says "RELATED QUESTIONS". Click on the first question, of Please help with Calculus?? Then go to Steve, Friday Nov 8, 2013 and click on his link.
You can see the table working for you!!!
2.01
a fertilizer manufacturer buts a certain raw material by weight. Each batch of raw material purchased is weighed and the weight is recorded to the nearest pound. It is assumed that the round off error is uniformly distributed in the interval from -0.5 to 0.5. We wish to know the mean round off error and know the standard deviation of the round off error?
0.9
0.23
1. To calculate the mean, we can use the fact that the round-off error is uniformly distributed between -0.7 and +0.7. The mean of a uniform distribution from a to b is given by the formula:
Mean = (a + b) / 2
In this case, a = -0.7 and b = 0.7. Plugging in the values, we get:
Mean = (-0.7 + 0.7) / 2 = 0 / 2 = 0
Therefore, the mean of the round-off error is 0.
2. The standard deviation of a uniform distribution from a to b is given by the formula:
Standard Deviation = (b - a) / √12
In this case, a = -0.7 and b = 0.7. Plugging in the values, we get:
Standard Deviation = (0.7 - (-0.7)) / √12 = 1.4 / √12 ≈ 0.404
Therefore, the standard deviation of the round-off error is approximately 0.404.
3. The graph of a uniform distribution from -0.7 to +0.7 would be a rectangular shape, with equal height throughout the interval and zero height outside the interval. The x-axis represents the round-off error, and the y-axis represents the probability density function. The graph would look like a rectangle with width 1.4 (from -0.7 to 0.7) and height 1/1.4 (to make the total area under the curve equal to 1).
To calculate the mean and standard deviation for the round-off error in this scenario, we can use the properties of a uniform distribution.
1. Calculate the Mean:
The mean of a uniform distribution can be determined by using the formula:
Mean = (a + b) / 2
where "a" and "b" represent the lowest and highest values of the interval, respectively.
In this case, the interval for the round-off error is from -0.7 to +0.7.
So, a = -0.7 and b = 0.7.
Mean = (-0.7 + 0.7) / 2 = 0 / 2 = 0
Therefore, the mean of the round-off error is 0.
2. Calculate the Standard Deviation:
The standard deviation of a uniform distribution can be calculated using the formula:
Standard Deviation = (b - a) / √12
where "a" and "b" represent the lowest and highest values of the interval, respectively.
In this case, a = -0.7 and b = 0.7.
Standard Deviation = (0.7 - (-0.7)) / √12
Standard Deviation = 1.4 / (√12)
Standard Deviation ≈ 0.4028
Therefore, the standard deviation of the round-off error is approximately 0.4028.
3. Draw the Uniform Graph:
Since the round-off error is uniformly distributed in the interval from -0.7 to +0.7, we can represent this graphically using a rectangular-shaped probability density function (PDF), as the values are equally probable across the interval.
To draw the graph, we can plot the x-axis with the interval values (-0.7 to +0.7) and the y-axis with the corresponding probability density. Since it is a uniform distribution, the probability density will be constant.
Thus, the graph will be a rectangle with a width of 1.4 (representing the interval from -0.7 to +0.7) and a constant height of 1/(b - a) = 1/1.4 = 0.714.
Please note that the height of the rectangle on the y-axis should be adjusted based on the scale of the x-axis in order to maintain correct proportions.
Visualizing the graph would help in understanding the distribution and the probabilities associated with the round-off errors.