# Stats

posted by .

A bottling company uses a filling machine to fill glass bottles with mango juice. The bottles are supposed to contain 300 milliliters (ml). In fact the amounts vary according to a normal distribution with mean = 298 and standard dev = 3 ml. What is the probability that an individual bottle contains less than 295 ml?

Part 2 - What is the probability that the average content of a 4 pack of bottles is less than 295 ml?

With one bottle, you can use the Z-score.

Z = (X - mean)/SD = (295 - 298)/3 = -3/3 = -1

If you have memorized the major divisions of the areas in a normal distribution as indicated by the standard deviation (SD), you would know that 16% of the scores lie below this point = .16.

If you don't know these proportions, consult a table in the back of your statistics text called something like "areas under the normal distribution."

For the 4 bottles, you use the same formula. However, this time — since you are dealing with a sample mean rather than just an individual score — instead of dividing by the SD, you divide by the standard error of the mean (SE).

Z = (X - mean)/SE, where

SE = SD/sq.rt. of N

Solve for Z and look it up in that table to get your answer.

I hope this helps. Thanks for asking.

## Similar Questions

1. ### Statistics

A bottling company uses a filling machine to fill glass bottles with mango juice. The bottles are supposed to contain 300 milliliters (ml). In fact the amounts vary according to a normal distribution with mean = 298 and standard dev …
2. ### Statistics

A bottling company uses a filling machine to fill glass bottles with mango juice. The bottles are supposed to contain 300 milliliters (ml). In fact the amounts vary according to a normal distribution with mean = 298 and standard dev …
3. ### Math-Value of Mean

A brewery has a beer dispensing machine that dispenses beer into the company's 12 ounce bottles. The distribution for the amount of beer dispensed by the machine follows a normal distribution with a standard deviation of 0.13 ounce. …
4. ### stats

A company that manufactures and bottles apple juice has a machine that automatically fills 16-ounce bottles. There is some variation, however, in the exact amount of juice dispensed into each bottle. From a large number of observations …
5. ### statistics

Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.44 ounces and a standard deviation of 0.06 …
6. ### Stats.

Another one that I need help.... At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml. (a) …
7. ### statistics

A bottling commpany produces bottles that hold 10 ounces of liquid . Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 25 bottles and …
8. ### Statistics

A filing machine designed to fill soda bottles with 16 ouncesof soda. The distribution for the weight of the bottles is normal. Twenty bottles are selected and weighted. The sample mean is 15.3 ounces and the standard deviation is …