Hi Bob,
Thanks for the direction. I got so far with it on my own and became stuck. I did as you said but still have one question. Would the answer to the question be 1.31 ounces or 6.61 ounces? I feel the answer is 1.31. Thanks
* Statistics - bobpursley, Wednesday, October 6, 2010 at 4:56pm
No. When the mean is zero, the point comes out to be -1.31 ounces. But you want that -1.31 to be 5.3, so you add 5.3 to 1.31, mean 6.61. That way, you at 5 percent is still -1.31 ounces below the mean.
Remember here, you std deviation is .8 ounces, so three standard deviatons is only about 2.4
Ok so the average weight of the product should be around 2.4? Sorry I am just hitting a wall here. I see everything above and it makes sense but I just am struggling to know what the final answer is
No, the average is 6.61 (the mean). You want no more than 5 percent to be greater than 5.3ounces. With a .8 standard deviation, 5.3 is (1.31/.8=1.6 standard deviations from the mean.)
Go back to http://davidmlane.com/hyperstat/z_table.html the first applet, mean 0, standard deviation .8, below -1.31 and note that the shaded area is .05 That is what you wanted.
your mean: 6.61, std deviation .8
Think all this out, it is very important you understand the distribution curve.
Take a for instance: if you wanted no more than five percent to be 23, what would be the mean? Answer: -1.31 from mean is 23, so mean is 24.31
Based on the information provided, it seems that the final answer should be 6.61 ounces. Let me explain the reasoning behind this.
The previous discussion mentioned that the mean is zero and the point comes out to be -1.31 ounces. However, you desire that -1.31 to be 5.3 ounces. To achieve this, you need to add 5.3 to the existing -1.31 ounces, which gives you 6.61 ounces.
It's important to note that the 5.3 ounces in this context represents a desired value that you want to be 5 percent below the mean. By adding it to the initial value of -1.31 ounces, you can ensure that the resulting value is still 5 percent below the mean.
In terms of the average weight of the product, the information provided doesn't explicitly state it. Therefore, it's not possible to conclude that the average weight should be around 2.4 ounces based solely on this given information.