Assume 20 oz. cola bottles are filled so that the mean amount of liquid contained in the bottle is 20 oz and the standard deviation is .12 oz.
If a bottle is randomly selected, find the probability that the number of ounces in that bottle is greater than 20.21 oz.
I find the following applet very useful for these kind of problems
http://davidmlane.com/hyperstat/z_table.html
In case you do not have a computer available in the future, here is another way to solve the problem. Caculate the Z score.
Z = (X-μ)/SD = (20.21-20)/.12
Look up that Z score in a table in back of your statistics text labeled something like "areas under the normal distribution." Pick the value in the appropriate column.
I hope this helps a little more. Thanks for asking.
To find the probability that the number of ounces in a randomly selected bottle is greater than 20.21 oz, we can use the z-score and the standard normal distribution.
The z-score measures how many standard deviations an observation is from the mean. In this case, we need to calculate the z-score for 20.21 oz using the formula:
z = (x - μ) / σ
Where:
x = 20.21 oz (the value we want to find the probability for)
μ = 20 oz (mean amount of liquid in the bottle)
σ = 0.12 oz (standard deviation)
Plugging in these values:
z = (20.21 - 20) / 0.12
Calculating this equation, we find that the z-score is approximately 1.75.
Now, we can use a standard normal distribution table or a calculator to find the probability corresponding to the z-score of 1.75.
Using a standard normal distribution table, we can find that the probability corresponding to a z-score of 1.75 is approximately 0.9599. This represents the probability of the number of ounces in the bottle being less than 20.21 oz.
However, we're interested in the probability that the number of ounces in the bottle is greater than 20.21 oz. To find this, we subtract the probability we just found from 1 (since the total probability is 1).
So, the probability that the number of ounces in a randomly selected bottle is greater than 20.21 oz is approximately 1 - 0.9599 = 0.0401, or 4.01%.