# Normal Distribution Problem

1. Oct 19, 2009

### RedPhoenix

Been having an issue with these specific homework problems. Can you give me some insight on where to start.

#4.78 F

The actual amount of juice that a machine fills the juice boxes with is 4-ounces, which may be a random variable with normal distribution of $$\sigma$$ = 0.04 ounce

a) If only 2% of the boxes contained less than 4 ounces what is the mean/average fill on the juice boxes

b) If the variability of the machine that fills the boxes are reduced to 0.025 oz, confirm that the lower required average/mean amount of juice to 4.05 oz and keeping the 98% of jars above 4 oz

2. Oct 19, 2009

### honestrosewater

I am new to statistics, so ignore this if it doesn't make sense. What they say doesn't really make sense to me anyway. But do you have a standard normal table (or application)? It sounds like they are giving you enough to solve a standard z-score equation -- 2% of the population should fall below the z-score of x = 4 oz. with $\sigma$ = .04:

$$\frac{4 - \mu}{.04} = z$$

Look up what z-score has 2% of the area to its left.

3. Oct 19, 2009

### RedPhoenix

I dont have a table handy, but how can I find $$\mu$$?

I know its E(x).. or atleast I think so. I also know that the problem is written poorly and the book is not much better.

4. Oct 19, 2009

### honestrosewater

You can find tables and calculators online by googling, e.g., "standard normal table". Do you know what I am talking about, though?

You can find $\mu$ by finding the z that you need and plugging it into the above equation. Imagine the standard normal distribution. Do you know what this (bell) curve looks like? Put it in the Cartesian coordinate system so that the curve sits on the x-axis and the mean lies on the y-axis. You need to travel along the x-axis to the point where you can draw a line parallel to the y-axis and it will divide the curve into two figures such that the area of the figure on the left is 2% of the area of the original distribution curve. You express the distance that you have to travel in terms of standard deviations. Does this make sense?

To find exactly how far you have to travel, you can go http://davidmlane.com/hyperstat/z_table.html" [Broken], scrolll down to the second graph, type ".02" into the "Shaded Area:" box, and click the "Below" radio button. This will shade the graph and give you the number of (standardized) standard deviations from the mean that you have to travel, i.e., your value for z.

I am pretty sure this is the right approach because the answer that I got makes sense with part (b) of your question.

Last edited by a moderator: May 4, 2017