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A specialty foods company mails out gourmet steaks to customerswilling to pay a gourmet price. The steaks vary in size, with amean uncooked weight of 2 pounds with ...

Question

A specialty foods company mails out gourmet steaks to customerswilling to pay a gourmet price. The steaks vary in size, with amean uncooked weight of 2 pounds with a standard deviation of 0.10pounds. Use a normal model for the weight of a steak.Estimate the probability that a steak will weigh less than 1pound. Estimate the probability that a steak will weight between 1.5and 2 pounds. a.What is the expected rate of return?b.What is the standard deviation of the rate of return?

A specialty foods company mails out gourmet steaks to customers willing to pay a gourmet price. The steaks vary in size, with a mean uncooked weight of 2 pounds with a standard deviation of 0.10 pounds. Use a normal model for the weight of a steak. Estimate the probability that a steak will weigh less than 1 pound. Estimate the probability that a steak will weight between 1.5 and 2 pounds. a. What is the expected rate of return? b. What is the standard deviation of the rate of return?



Answers

Salmon A specialty food company sells whole King Salmon to various customers. The mean weight of these salmon is 35 pounds with a standard deviation of 2 pounds. The company ships them to restaurants in boxes of 4 salmon, to grocery stores in cartons of 16 salmon, and to discount outlet stores in pallets of 100 salmon. To forecast costs, the shipping department needs to estimate the standard deviation of the mean weight of the salmon in each type of shipment
a) Find the standard deviations of the mean weight of the salmon in each type of shipment.
b) The distribution of the salmon weights turns out to be skewed to the high end. Would the distribution of shipping weights be better characterized by a Normal model for the boxes or pallets? Explain.

Okay for this problem, We're gonna refer back to some context from a previous problem. And we're gonna do some adjustments to Simeon information that we know about cattle. How spears ever sold at auction. So, um, we're told Angus, wait the mean weight of it. Yearly, Angus steers as £1150. It's on average, these cattle and the standard deviation of £84. And what we want to know in this case is we want to know, um, we want to know they want to sell £1000 cows, so they want their cows to be over £1000. What they're gonna do is going to subtract £1000 for me to see way Know how that's gonna change the mean. So that's we're going to do for this problem. So they're trying to get us to see that the effect on the information and then we're also going Teoh, someone wants to find me and standard deviation. Um, and they want to be a little bit cost analysis on this, too. So let's go and do this right at the end. So we're gonna do this. We're going to say, Well, Let's take this in our plan for this problem. I mean, finest £1 do that just to me. We want to know what the mean is going to be for you. Take. Cows are only over 1000. So we could take our 11 52 minus 1000. So now you know I knew me people's to one her, right. So you do. That means you just take the disaffected itself in your transformation. So that's how the mean was 11. 52. We could take away 1000 and 152. Thea other question is, what's the standard deviation now? The standard deviation is £84. Why is that true? Because the standard deviation is unchanged. You know, we're adjusting the weight by 1000 difference. That it varies from one of the mean is it does not change. That's an important fact to know for part of the problem. New me is used in a deviation. So for for part B, we were told that we have a 40 cents per pound is how much they're going to make it. We sell these cattle. So what we can do, Harby, is we gonna take this original cost too. So we can do with this is 11. 52. I was 40 cents a pound, taking kind of data transforming it. Really? What we do is able to my multiplying constant. Um, you can do that with your statistics. So 11 52 times that is just going to say, on average, uh, if you sell cattle that that's that we it's before 60 dollars and 1980 cents. What you would make for a typical bringing weight cow and we're going to see is that other fact of the £84 with standard deviation. So the question said, uh, standard deviation of the sale prices for all steers. So this standard deviation sale price that's the mean steel price. Standard deviation sale price just equals to that 84 £84. Standard deviation repents 40 cents, assuming that multiplication for that, too. So you can take that a four times 40 cents. That gives us $33.60. So that's that

Questions or, um, a B C. So for part A, they are asking us what kind of distribution it is and with being uniformed distribution, Uh, each one is equally likely. So that means it's uniformity even say it's uniform. So we go from 24 26 with a mean of 25 and they want the standard deviation. The verse standard deviation were using the formula being my most a one of next year over 12. So here I have, uh, 26 minus 24 water. I swear, over 12. And it's where word of that so that becomes to square, which is four over 12 ends. Where of that. So it's really this where we're 1/3 which equals by 77 or so My standard deviation. Wait, I 774 in r B. They want us to find it in a normal distribution for a normal distribution. I would have. I mean, you know, 25 they mean but my standard deviation would be my standard deviation divided by the square root of and so my standard deviation with 0.5774 divided by this, we're route of 100 which I know to be 10 so 0.5774 divided by 10 gives me a week zero by seven cabin. So for part B, I have a normal distribution. 25 is my name. Wait, 05 77 is my standard deviation. And for part C, we're looking at a probability. Find the probability, which means normal. See? Yeah, I'm going to go lower. My lower bound is negative Infinity and I usually just put in the year 99999 You put in native one e 99 It just represents negative infinity. And in here we have our upper bound at 24. Weight now are mean and our standard deviation. And when we do all that, you should that zero for one five.

Hi. We've been asked Toe shoes and the pipa. This is for this question. So we know that the alternative is cinema is greater than 4 to 5. Alfa is born. One on the sample size is 20 eso I use the formula to compute the Ah, but this statistics are funded. That's 37.24 on. As you see here, we have a greater than so we are in the right tail case on I'm gonna use now the p value omitted. So I know that's the This is the statistics on I have that degree of freedom is 19 since it is in minus one. So 19 and I found that. Okay, we are 37.24 So we are somewhere here, so I know that my P value is less than 0.1. So my, uh, decision is, uh, reject. On the other method is the classical method. So I have to find what we call the critical value on. I know that's my given alpa's 0.1. So his 0.1 and here's the degree of freedom is 19. So it's 27.2 on, As you see here I again my just statistics as 37 on it is way greater than that critical value. So we have the same conclusion here.

All right. So, We have individual weights here. So we know that the mean of these individuals is 1450 g and that the standard deviation is 250 g. All right. So, we want to know the probability that you have an individual that weighs more than 700, g, g. Okay. Now, since these are normally distributed, we can use the normal distribution formula where the the grams that we care about going places. A You always subtract the mean and divide by the standard deviation. Okay, so for our problem, We have 1700 -1450 over 2 50. All right. So, if you simplify the inside of the parentheses, we get to 50 divided by 2 50 which is one. And that's the Z value. This number. This a minus new. Over the standard deviation. That is the z value. Okay, So is the value of one. If you look look that up on a table of Z values in the back of your book, you'll find that Z Z 11 has uh 84.13% chance Of being 1700 g. And here's the kicker or less. All right. But we care about more any time. It is a greater than you have to take the probability you got and subtracted from one. All right. And that will give you your correct answer here. So, we're actually get an answer of 15.87%. All right. For part B. We have Less than 1250g. All right. Since this is less than you just plug it in and the number from the table is your final answer. So 1250 -1450 over 250. Alright. And 12 50 minus 14 fifties negative 200 over 2 50. This gives you a Z value of negative 200 over 2 50 is negative 500.8. And so our final answer, If we look up negative 0.8 on RZ Table, we get 21.19%. All right. 21.19% of uh individuals in this group are less than 12 50 g. 1000 and 50 g. And then finally part C. Wants to know what percentage are between 1116 100 g. All right. When you do this, whenever you have a range of values like this, you always take the biggest the 1600 subtract the percentage you get from that. Subtract the percentage of the smaller 1100. All right. So let me step you through the 1600 minus 14 50/2 50. All right. Just like we've been doing now, you subtract the 1100 now. Okay, So, this first one gives you 1600 miles 14 50 is uh 1 51 50 divided by 2 50 is 500.6 A z value of 0.6 and the second one gives you a Z value of negative one. All right, If you do the math inside of the parentheses, so on our table, a value, Z value 0.6 is 72.57%. And the value of negative one is 15.87%. So these must be subtracted, so 72.57 -15.87 is 56.7%.


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