# Statistics - bobpursley, Wednesday, October 6, 2010 at 4:30pm
second applet.
Set mean to zero, std deviation to .8 oz
check below
enter shaded area .05
Notice the answer comes up 1.31 ounces. So the mean must be 5.3+1.31=6.61
Put that in for the mean, and verify.
You should be able to do with with your calculator also, grab your book and read. Finally, you may be learning to do this with tables...for that, hump, grunt, and strain through it.
# Statistics - Beverley, Wednesday, October 6, 2010 at 4:41pm
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
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
The answer to the question is actually 6.61 ounces. Let me explain how to arrive at that answer.
Based on the information given, you are dealing with a normal distribution with a mean of 0 and a standard deviation of 0.8 ounces. You want to find the value that corresponds to a shaded area of 0.05.
To find this value, you can use a Z-table or a calculator that has a normal distribution function. The Z-table is a table that provides the probability of finding a value less than a given Z-score in a standard normal distribution.
In this case, you want to find the Z-score that corresponds to a shaded area of 0.05. The shaded area represents the probability of finding a value less than a certain Z-score, so you want to find the Z-score that corresponds to a cumulative probability of 0.05.
Using a Z-table, you would look up the Z-score for a cumulative probability of 0.05. The Z-score you find is approximately -1.645.
Once you have the Z-score, you can use the formula Z = (X - μ) / σ to find the corresponding value, where X is the value you want to find, μ is the mean, and σ is the standard deviation.
Rearranging the formula, you can solve for X: X = Z * σ + μ.
Plugging in the values, you get X = -1.645 * 0.8 + 0 = -1.316.
Since the mean is set to 0, you then need to add this value to the mean to find the answer: X = -1.316 + 6.61 = 5.294. Rounded to two decimal places, the answer is 6.61 ounces.
So, in summary, the answer to the question is 6.61 ounces, not 1.31 ounces.