Question 1182078: Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 8 grams of fat per pound. A random sample of 36 farm-raised trout is selected. The mean fat content for the sample is 29.7 grams per pound. Find the probability of observing a sample mean of 29.7 grams of fat per pound or less in a random sample of 36 farm-raised trout.
Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
Found 3 solutions by ikleyn, greenestamps, math_tutor2020:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
I tried to solve the problem several times.
But every time, as I see this idiotic dimension "grams per pound", I become laugh and can not stop.
Post this problem to some comics magazine for a contest.
It may win a "Shnobel prize" there ( ! ) . . . with the formulation "for invention new unit grams per pound" . . .
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This units "grams per pound" is formed using units of mass from different measuring systems.
I worked more than 40 years in Science and Engineering, learned Physics fundamentally in school and at the University,
read thousands of articles on these subjects, and NEVER saw such or similar
combination of units for the same Physical quantity from different measuring systems in one problem.
It is the same as to go walking on the street wearing yellow black check shorts, one sock green and the other red,
left shoe on the right leg and right shoe on the left leg.
It is good for a clown in a circus, but not for other purposes.
The other tutors think that it is possible.
Sure, it is possible - but all other people will look at you adequately . . .
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Sorry you went to the trouble of posting your question only to get a response calling the post comical.
It makes perfectly good sense to say that the fish contains a certain number of grams of fat per pound of fish.
So re-post your question and let somebody help you with it.
Sorry, the question is not for me -- I know very little about probability and statistics.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
The figure "70 million" isn't used at all. It's just filler and a distraction.
The value 32 will be used and that's the value of mu (population mean).
mu = 32
This is from previous data of other studies
Another parameter we use is
sigma = 8
again determined from previous studies. This is the population standard deviation.
In this current study, n = 36 is the sample size
The xbar, aka sample mean, value is 29.7
Recall that the xbar distribution is simply a distribution where all the xbar values are plotted in pretty much a historgram fashion. Your teacher wants to know what are the chances of observing xbar = 29.7 or smaller. If you were to throw a dart, what are the odds of landing somewhere at or below 29.7?
In symbolic terms, your teacher wants to know P(xbar <= 29.7)
First we'll need to convert to a z score
z = (xbar - mu)/(sigma/sqrt(n))
z = (29.7 - 32)/(8/sqrt(36))
z = -1.725
z = -1.73
Now use a table such as this one here
https://www.ztable.net/
Select the row that has -1.7 at the left edge. Select the column that has 0.03 at the top. The intersection of these rows and columns tells us the approximate answer we're after. That value being 0.04182
So P(xbar <= 29.7) = 0.04182 approximately
This rounds to 0.042
If you were to use your TI calculator, then you'd use the normalCDF function. Type in normalCDF(-99,-1.725) to get roughly 0.04226
which is fairly close to what the table says. There's going to be some discepancy because I had to round -1.725 to -1.73 in order to use the table. It will depend on what your teacher wants (whether to use a calculator or table) as which answer you ultimately go for. I would ask your teacher for clarification if possible.
Luckily, with either case, they both round to 0.042
Answer: 0.042
There's about a 4.2% chance of getting a sample mean of 29.7 grams per pound fat content or less.
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