5

A particular fruit's weights are normally distributed, with amean of 271 grams and a standard deviation of 27 grams.If you pick 3 fruit at random, what is the ...

Question

A particular fruit's weights are normally distributed, with amean of 271 grams and a standard deviation of 27 grams.If you pick 3 fruit at random, what is the probability that theirmean weight will be between 246 grams and 249 grams

A particular fruit's weights are normally distributed, with a mean of 271 grams and a standard deviation of 27 grams. If you pick 3 fruit at random, what is the probability that their mean weight will be between 246 grams and 249 grams



Answers

Certain coins have an average weight of 5.201 grams with a standard deviation of 0.065 g. If a vending machine is designed to accept coins whose weights range from 5.111 g to 5.291 g, what is the expected number of rejected coins when 280 randomly selected coins are inserted into the machine?

So we know that individual Candies are normally distributed. So this is for individuals. And we know that the mean weight of an individual candy is 0.1 out. And we know that the standard deviation of an individual candy is point 01 ounces, and we're going to have 16 pieces of candy placed into a passion package. And it tells us that these are independently placed in, which is important. And so our new distribution will also be normal because the original distribution was normal. So this distribution will be normal. And our first questions we want to know what will the mean B and I'm going to let that distribution be called why? And really are written a variable. Why is the sum of 16 independent Candies and there are 16 of these? And so the mean will end up being 0.1 added together 16 times or 160.1 time 16 So it will be 1.6 ounces. That will be the mean of our distribution. Now, what would the standard deviation be? Well, the important part was that these were independent because if they weren't, we wouldn't be able to find the standard deviation and so remember, for a random variable to find the variance or the standard deviation squared, we have to find the standard deviation of each of these individuals added together all the way out to the last one. And so our standard deviation of why will end up being 0.1 squared plus point Oh, one squared plus and so on. And we'll add together 16 of those so we can go time 16, and then we will need to square root that and so we'll end up having if we we can do this actually without using a calculator. The square root of this becomes 0.1 and the square root of 16 becomes four. And so our answer is 40.4 ounces. That will be our standard deviation for this distribution. So here is the mean for an individual and the standard deviation for an individual candy. And if we put 16 of those Candies in the mean weight of that package, just the candy itself will be 1.6 ounces on the average and the standard deviation weak 0.4 now. So that was part a part B. We wanted to find What's the likelihood that the weight of the package is less than 1.6 ounces and that's going to be 50%? Half of them will be less than that. So be 50% and then we want to find what number? What what? Wait has 99% of these packages are higher than that? So I go back up to our picture. Well, we'll just we'll just draw the one. And we know that the mean is 1.6, and we want 99% or this area to be 0.19 point 99 which means this area down here must be point or one. So we need to find what that Z value is because we know we're working with a normal distribution and so we can look that either up in a table or I'm going to use my inverse normal function on my calculator and type in an area of point a one keeping the main at zero and the standard deviation at one, and we'll find out what that Z value is, and that's the value is negative 2.3 to 6. So let's now convert that into knowing that a Z score is equal to the score. Well, we is why, minus the mean divided by the standard deviation. And we know that that Z score is negative 2.3 to 6, and we're going to find that y value and we know the mean is 1.6. And the standard mediation is point oh four. So we can take this number negative 2.3 to 6. Multiply it by point oh four and then add on 1.6 to solve for life. And we find out that why is equal to 1.5 Yeah, 1.507 ounces. So roughly 1.5 ounces If the pack, if you're weight of the candy 99% of the time the weight of that can be The package of 16 Candies will be higher than 1.5 ounces. And I think we've answered all the questions

Okay for this problem. We're giving some given some apple information, water, watermelon information. And we know you're a normal distribution. So we need to do is break this into steps and kind of the first step is always sketching out what we have and then figuring out what we know and what we want to know. This problem is a little different than some of the preview problem previous problems, because we we want to know in this case is the mean We don't know the mean, So we can't go forwards and just figure it out. But we do know the standard deviation for this problem. And we know some information about, um how 3% weighing less than £15 for these watermelons. So let's write down this s standard deviation information. So what? It Whatever this the mean is if we take me and plus or minus, uh, Senator Vision would add £2.8. Eso No, this problem gives us this piece of information, so I like to sketch it on the diagram itself. So they said we don't know what the mean is, but we do know that 3% way less than £15 over here. £15. We know that less than 0.3 way less than £15. So we're gonna use that information. I'm going to my calculator to work backwards from a normal distribution because the calculator will help us to be like reading the table three. In our book, we're gonna work backwards and figure out a Z score that corresponds to the to this £15 weight, and then we will find the unknown mean, So let's go over here and do the second distribution. Second universe, second distribution, inverse norm. So what we're gonna do is we're gonna have the area 0.3 So what? I have drawn and green over here, and we're gonna leave the zero on one because we don't know what it is, but we get a Z score from this. So this will give us disease score that corresponds to that £15 weight there and that we weaken a little bit of math after that and figure out what our meanness. So we know the Z score that goes with that is Z score that goes with this 15 and it makes sense since its negative, so we know the Z score that goes with the £15 weight equals two negative 1.88 and we know for an easy score. We know the Z score is just nothing more than me than the value that we know, minus the mean divided by the standard deviation. So what we can do is, if we want to find out with this blue, we want to find out. Is that the black since there want to find out this. So let's put in the values that we do know and work backwards to figure it out. So keep this unknown numbers here like, um red. So negative 1.88 uh, equals two R X guy, which is at 15 pounds watermelon. That's what the mean is which we don't know, divided by the 2.8 plus of minus standard deviation above the mean. And so not only is my calculator after the size since negative 1.8 eights already in my calculator and I want to solve for the mean take a negative 1.88 and multiply by two point under the 2.8 get the evening alone. So before you go do far right back down, so we'll say that's a negative. Five point 26 approximately equals to 15 minus that mean value. And I Really what I do is that add the Muto that side and then ah, have a positive mean value and then added by 15.26 to 15. So I just do this. Let's just do 15 plus the five point 26 that's going to give us the mean value, just 20 which makes sense. It's 15 over their twenties in the middle, so we now know that we add that sure work years we're gonna have 15 double sides to a little bit of negative stuff and took care of the negatives, the calculator of what I said out loud. But basically the mu equals to 20.26 So put it over here. So with this problem, that's the mean what we want. 20.26 So it was a mean weight of the apples of the watermelon and there we have it backwards from are known percentiles, too. Use the relationship of disease for to find an unknown mean

Okay for this problem. We're giving some watermelon information, and we told it's normally distributed. But what's interesting about this problem is that we don't know the mean for it, so we know we have watermelon distribution, and we know the standard deviation for it. So the standard deviation for that is plus or minus £2.8 for these ripe watermelons we want to find out is we want to find out what the means for is now the most useful in piece of information here is we're, um we know that 3% way less than £15. So we actually do know this £15 mark over here and 3% way less than that. So our plan for this problem is going to be, too. Since we can figure out the area that corresponds to 3% you can find a Z score for the 3% and then we can figure out the meat weight is So I use my calculator over here, and it was called the Universe Norms that we're gonna inverse when work backwards off of our known information can figure out with the area that corresponds to 3% is and we know the area poor corresponds to 3%. We're gonna find out the value that goes with 3%. And so we know that 3% value goes with the Z score of negative 1.8 somebody's e 15 here because what that meant was his £15 apples. Since we knew the apple information for this problem, I mean watermelon, not at all. So that's negative. 1.88 So our next step here, the first step was to get that Z, that's a Z score. Their money there is the ah formula to figure out the unknown mean problem there. So we know any of these four equals two. The number we know. So I was gonna go attacks here. There. We know my Aniston. I mean, divided by the standard deviation of this problem. Really, we're trying to find is the the mean So let's put in the values we know negative 1.88 And we know the negative 1.88 forest corresponds to the 15 there, minus the mule, divided by the 2.8 standard deviations for this data. Someone who's my calculator now. Ah, So if I understand a little bit of algebra to get this alone. I need to multiply both sides by 2.8. So I'm just gonna hit the times, and that will give me we have over here in the left side of my equation. Equals to 15 minus meal. Okay. Is it? Technically, I would add the mean to the right side of the left side of the equation and then add the 5.2662 figure with them. You is. So let's just do this here, Um, you eagles to whatever. The 15 plus 2 5.26 sixes. So I'm gonna take that answer. And I wasn't going to be tricky there, but I messed myself up. Welcome news. I wrote it down. Okay, so 5.266 is what I need to do. So, any 5.266 need Adebowale sides? Really? What that means is I'm at about 2 15 and so that's going to be my final meet. Answer. Uh, which is 20 points to six. So 22.6 is the mean weight of the watermelons. The unknown mean Wait

Yeah. The weight of a jam as normal distributed with Main 16 and standard division point to to compute these probabilities. We can transform the normal distribution into a standard normal distribution. That is. We subtract the main and then divided by the standard deviation. So this probability he calls this probability. Since it is a standard normal distribution, we can use a table in appendix C. You know from that table, we know there are this probability, yes. 0.30 85 for part B is similar. This is a probability of standards normal distribution from the table in appendix C. This probability is point 15 87


Similar Solved Questions

5 answers
EXAEEPLEProve that the Ilmit does not exlst,lim = -3 SOLUTIONlimLillitSince the riqht- and left-hand Ilmits are different; follows from Theorem that the Ilmit does not exist. graph of the function f(x) 1/ (* * 3) to the left supports the one-slded Ilmits that we tound
EXAEEPLE Prove that the Ilmit does not exlst, lim = -3 SOLUTION lim Lil lit Since the riqht- and left-hand Ilmits are different; follows from Theorem that the Ilmit does not exist. graph of the function f(x) 1/ (* * 3) to the left supports the one-slded Ilmits that we tound...
5 answers
QuesTiomfomedonan objcct that has height ol 12 cm, the irnage virual and the converging lons has . focal length o/ 22 cm image image 13 cm Irom the whal is the height of the[ image? 7.54 c19cm12 cm36 cmquestion ?has an object 20 cm E front accone converging lens diverging lcns {=-15 cm the lens seperation is 30 cm what Is Ine Iinal image posilion?15 cm , placed scries with Ihe @rst Ions12.8 cm8.57 cm245 cm
quesTiom fomedonan objcct that has height ol 12 cm, the irnage virual and the converging lons has . focal length o/ 22 cm image image 13 cm Irom the whal is the height of the[ image? 7.54 c 19cm 12 cm 36 cm question ? has an object 20 cm E front accone converging lens diverging lcns {=-15 cm the len...
5 answers
Find particular anti derivative function ofC' (x) = 4x + 5x - 3x-2, C(2) = 4
Find particular anti derivative function of C' (x) = 4x + 5x - 3x-2, C(2) = 4...
5 answers
The Cumec IUPAC name following compound oruthe bondling formula is (3 pls)CH-cln-Cl-CH = IC-CH;ahis [u 4 KreC8lcs
The Cumec IUPAC name following compound oruthe bondling formula is (3 pls) CH-cln-Cl-CH = IC-CH; ahis [u 4 Kre C8lcs...
5 answers
Evaluate JJ (o,0,)+ ndS where S is the surface of the cone z = Vr +y 0<2<3_
Evaluate JJ (o,0,)+ ndS where S is the surface of the cone z = Vr +y 0<2<3_...
5 answers
(14 points) Evaluate F dr for F (cy, 22,3y) and C the curve of intersection of 22 +y? = 9, 2 +2 =5.
(14 points) Evaluate F dr for F (cy, 22,3y) and C the curve of intersection of 22 +y? = 9, 2 +2 =5....
4 answers
Woman forgets to turn off the headlights of her vehicle while it is parked in garage. If the 12.0 V battery in the vehicle is rated at 66.0 A and each headlight requires 28.8 W of power; how long (in hours) will it take the battery to completely discharge? (Assume the headlights are connected in parallel:)hours
woman forgets to turn off the headlights of her vehicle while it is parked in garage. If the 12.0 V battery in the vehicle is rated at 66.0 A and each headlight requires 28.8 W of power; how long (in hours) will it take the battery to completely discharge? (Assume the headlights are connected in par...
4 answers
Furrow formation does not occur in plant cell during cytokinesis because of(a) Extensible cell wall(b) Inextensible cell wall(c) Extensible plasma membrane(d) Inextensible plasma membrane
Furrow formation does not occur in plant cell during cytokinesis because of (a) Extensible cell wall (b) Inextensible cell wall (c) Extensible plasma membrane (d) Inextensible plasma membrane...
1 answers
How could you prepare the following compounds using a starting material containing no more than three carbons? A compound with the correct six-carbon skeleton can be obtained if a three-carbon aldehyde undergoes an aldol addition. Dehydration of the addition product forms an $\alpha, \beta$ -unsaturated aldehyde. Conjugate addition of $\mathrm{HBr}$ (Section 18.16 ) forms the target molecule.
How could you prepare the following compounds using a starting material containing no more than three carbons? A compound with the correct six-carbon skeleton can be obtained if a three-carbon aldehyde undergoes an aldol addition. Dehydration of the addition product forms an $\alpha, \beta$ -unsatur...
5 answers
Two cars are headed for the intersection of the two roads. IfCar A is travelling south at 45 km/h and car B is travelling eastat 60 km/h, at what rate is the distance between the carsdecreasing when car A is 9 km and car B is 11 km from theintersection? Note: Write only the numerical value of the rate, theunits are already written. Write the exact answer not the decimalapproximation (for example write 45 not 0.8).
Two cars are headed for the intersection of the two roads. If Car A is travelling south at 45 km/h and car B is travelling east at 60 km/h, at what rate is the distance between the cars decreasing when car A is 9 km and car B is 11 km from the intersection? Note: Write only the numerical value of th...
5 answers
The Class A balance has a sensitivity requirement of 6 mg, whatis the minimum weighable quantity in grams on this balance ,knowingthat the standard % error is 5%? No units. No rounding.
The Class A balance has a sensitivity requirement of 6 mg, what is the minimum weighable quantity in grams on this balance ,knowing that the standard % error is 5%? No units. No rounding....
5 answers
The average home in the U.S. is expected to cost $236,000. Arandom sample of 55 homes sold this month showed anaverage price of $229,000 with a sample standard deviation$33,000. We are interested in determining if the cost of theaverage home has decreased this month. What is the value of thetest statistic? (Round your answer to three decimal places.)
The average home in the U.S. is expected to cost $236,000. A random sample of 55 homes sold this month showed an average price of $229,000 with a sample standard deviation $33,000. We are interested in determining if the cost of the average home has decreased this month. What is the value of the tes...
5 answers
What is the best statistics definition of a sample?An individual unit of studyApiece of food you stole from your friend s plate to see if you like their food better than yoursA subset of a populationAll elements of interest
What is the best statistics definition of a sample? An individual unit of study Apiece of food you stole from your friend s plate to see if you like their food better than yours A subset of a population All elements of interest...
5 answers
~/6 POINTSLARSONETS 3.7.004.Assumn thatare both dlfferentiable furctions of and (Ind the required Values I00dyldt . and dxldt:(a) Fitd dyldt , Olven dyldtard dxkdt(6) Furd dx/dt, Oiven dxldtald dvfdtAnsumi
~/6 POINTS LARSONETS 3.7.004. Assumn that are both dlfferentiable furctions of and (Ind the required Values I00 dyldt . and dxldt: (a) Fitd dyldt , Olven dyldt ard dxkdt (6) Furd dx/dt, Oiven dxldt ald dvfdt Ansumi...

-- 0.024839--