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Thls EWciphten Avelar Proplemal iedsmotel hasMutelelsusually rents out; the following proporionssingles at: $60 per night 35%6 doubles a $74 per night 20%, trples a...

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Thls EWciphten Avelar Proplemal iedsmotel hasMutelelsusually rents out; the following proporionssingles at: $60 per night 35%6 doubles a $74 per night 20%, trples a 590 per nighiUse welghted average compute tne Average Rdom Rate per nightIhe motel has annual Ixed COSiS 0f $445,J0u and variai € costs averages 514 per ICOM occUpedCaculate the moter"$ breakeven level and ils cccupancy percentageCalculate the occupancy percenlage thal will provide operating iricoire (pefote tax) ol $65,000 ye

Thls E Wciphten Avelar Proplemal ieds motel has Mutelels usually rents out; the following proporions singles at: $60 per night 35%6 doubles a $74 per night 20%, trples a 590 per nighi Use welghted average compute tne Average Rdom Rate per night Ihe motel has annual Ixed COSiS 0f $445,J0u and variai € costs averages 514 per ICOM occUped Caculate the moter"$ breakeven level and ils cccupancy percentage Calculate the occupancy percenlage thal will provide operating iricoire (pefote tax) ol $65,000 year Caiculate the occupancy percentaqe necessarv provide an operating nccme (belare tax) Ol 565,000, If Ihe average room rale were cecreased by 20"8 Hint You can recompute Ihe we ghted average baseu (S60-512 and $90 $18-72) Oryou can use 48, 574-14.80-59.20, shortcul basec your knowledge Ol weighted average



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Assume that the population of $x$ values has an approximately normal distribution. Camping: cost of a Sleeping Bag How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from $20^{\circ} \mathrm{F}$ to $45^{\circ} \mathrm{F}$. A random sample of prices (\$) for sleeping bags in this temperature range was taken from Backpacker Magazine: Gear Guide (Vol. $25,$ Issue $157,$ No. 2 ). Brand names include American Camper, Cabela's, Camp $7,$ Caribou, Cascade, and Coleman. $$ \begin{array}{rccccccccc} 80 & 90 & 100 & 120 & 75 & 37 & 30 & 23 & 100 & 110 \\ 105 & 95 & 105 & 60 & 110 & 120 & 95 & 90 & 60 & 70 \end{array} $$ (a) Use a calculator with mean and sample standard deviation keys to verify that $\bar{x} \approx \$ 83.75$ and $s=\$ 28.97$ (b) Using the given data as representative of the population of prices of all summer slecping bags, find a $90 \%$ confidence interval for the mean price $\mu$ of all summer sleeping bags. (c) Interpretation What does the confidence interval mean in the context of this problem?

We want to find the sample mean X. Bar the sample standard deviation S. And construct a 90% confidence interval about the population, meaning you given the data below assuming that population is normally distributed. We then want to interpret the interval so we find expire and s using the appropriate definitions. X bar is simply to some of the data divided by N. In this case 83.75 the sample standard deviation S. Is the square root of a sum of deviations from the mean square divided by n minus one. In this case, 28.97 Next to solve the for the interval, we start by identifying the critical T score. We use a tea table from google or a textbook which maps the degree of freedom in this case 19 and the confidence level in 3.9 under the correct TC value in this case, 1.7 to 9. Next we construct the margin of error given by the formula. The left plugging in our T c r S and r N gives E equals 11.20 Now, we can solve for the confidence interval given formula experimental E is less than us an extra plus E plugging in our X bar. R E gives revenue 2.55 is less than you is less than 94.95 We interpret the signing as we are 95 90% confident that mu is between 72.55 and 94.95 That is, we are 90% confident that mu falls between these values.

All right, so we're given a set of them treatment costs. 10 of them were supposed to use thes sample one trees as a point estimate of the Sorry to find a point estimate of the mean and the standard deviation. So strong with our point estimate. Far the mean. We're just gonna add these up like so and then divide this by the number of entries, which is 10. You add up this top part, it becomes 45,000 500. Divide that by 10 and you get that your point estimate for the meanest 4550. All right, standard deviation, which is a much longer process. And I've already pre written part of it, just for the sake of gravity and me not having to transcribe everything. Ah, while trying to record. So anyway, here are all of our data points. What we do is that we subtract our point estimate for the mean from all these. So that's gonna be ah, negative. 1 74 cause off. 4376 minus 4550 is negative. 1 74 5578 Minus 4500 50 equals that and we keep going down the line like so. And then we're gonna square all these differences. And that's what you get here When you add all these up. That is a terrible looking Sigma. I'm sorry. Hold on. We're gonna rewrite that. Also, this brackets Not great either, but hey, whatever. Anyway, this adds up to 9,068,000 620. We're going to divide that by N plus one, which is 11 s o. We get that. Our, um point Usman for variance is one million. Ah! Oh, wait. Sorry. And minus one and plus one My bad, which is gonna be nine. Yeah. I was wondering why that didn't look right in my work anyway. Ah, that will be Let's see, one million. Ah, 7000 624.44 You take the square root of that you get s is equal to 1003 0.8. There you have it

For this problem, we have an of T, which stands for the number of personnel in the Navy in the thousands, depending on the year between the year 4007 when we have am of tea representing the number of personnel in the Marines, also in the thousands and so reporting we're going to find end plus m of tea. That would be the total number of Navy and Marines personnel together. So we have these two equations together and we get 0.2 to 70 cubed minus 4.11 t squared, plus 14.6 T plus 544 total personnel, Navy and Marines. Okay, so let's find the total personnel first. In different years, let's find a total personnel for AM or an A plus Amma of zero. That would be the year 2000. And so we have these together and we use a calculator. I'm using my calculators table feature to make this easier on me. Um, I go ahead and put zero and pretty. I get 544 so 544,000 and plus M of six would be for the year 2006. So we put six into our function and we get 532 0.6 7000 personnel and then an plus m of 12. So for some reason, we're being asked to find it for 12. Even though we're told the model is only useful from the years 2000 to 2007. That's okay. We get 519.62 1000 now for Part B. We're going to take the same two equations, and we're going to subtract them instead of adding them. And that's going to show us the difference in Marine and Navy personnel numbers so and minus M of tea. So when we subtract them, we get your 0.15 70 cubed minus 3.65 T Square plus 11.2 t plus 200. Okay, so that's the difference between Navy and Marines home. And then what we're going to do is find a difference for these years. We have Year zero, your your six and you're 12 again. I touched the function into my calculator, and I'm using the table feature for year zero. We get 200,000 is a difference in personnel for year six. That would be the year 2006. We get 169.7000 and her you're 12. That be the year 2012. We get 80.96 Looks like the difference between the two is decreasing and shouldn't say the rows, and it should say 1000 okay.

Mhm. For the problem, going to us here, we have the average daily rate of US hotels from 2000 and 6 to 2009. And this can be approximated by like giving function. So we want to know the average daily rate of US hotels in 2006, 2000 and seven and 2000 and eight. Well, we know that t equals zero is 2006, so that's going to be um F f T equals zero point 88 P squared plus 3.21 G. That's 96.75 Um And we're gonna evaluate this at f of, you know, we get this half of one, we'll get that enough of to get one of 6.69 That's in um Those are the daily rates. So sketching the graph of f, we end up getting this graph right here, but then there's obviously going to be another portion to it once we reach the value of two.


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