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Ntps{Aumathr cnusuidenMplaverhadedo DOn VcniTUR396ImBIO 500 (14)Cyntnia Shellenbanger ,Homework: Module 3 Homework Score: 0 of 15 pts 19 ot ?20 (18 complele) 6.5.15...

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Ntps{Aumathr cnusuidenMplaverhadedo DOn VcniTUR396ImBIO 500 (14)Cyntnia Shellenbanger ,Homework: Module 3 Homework Score: 0 of 15 pts 19 ot ?20 (18 complele) 6.5.15 An airlinier carrics 400 passengers and has doors wilh= height = 74 in. Hcights of men are normally distributed with meui 69.0 = Ifa male passeriger randomly sclected , find Ihe probability that he can through the doorway without bending The probability 9633 (Round to four decirnal places needed ) find the probability thal Ihe mean h

ntps{Aumathr cnusuidenMplaverh adedo DOn VcniTUR396 Im BIO 500 (14) Cyntnia Shellenbanger , Homework: Module 3 Homework Score: 0 of 15 pts 19 ot ?20 (18 complele) 6.5.15 An airlinier carrics 400 passengers and has doors wilh= height = 74 in. Hcights of men are normally distributed with meui 69.0 = Ifa male passeriger randomly sclected , find Ihe probability that he can through the doorway without bending The probability 9633 (Round to four decirnal places needed ) find the probability thal Ihe mean height of the 200 men less than 74in If half of the 400 passergers Men HN Scere: standard devietion 0f 2 &m Comdlede Eua tough The probability (Round to four decimal places a5 needed ) answer In the answer box and then click Check Answer Enter your Clear All



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Doorway Height The Boeing $757-200$ ER airliner carries 200 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 68.6 in. and a standard deviation of 2.8 in. (based on Data Set 1 "Body Data" in Appendix B). a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. b. If half of the 200 passengers are men, find the probability that the mean height of the 100 men is less than 72 in. c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why? d. When considering the comfort and safety of passengers, why are women ignored in this case?

73. According to a study done by Day Anza students, the height for Asian adult males is normally distributed with an average of 66 inches in a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X equal the height of the individual. Hey, X is gonna follow normal distribution. We're gonna have a means of 66 in a standard deviation of 2.5. Be find the probability that the person is between 65 69 inches. So want to find the probability that the person is between 65 at 69 inches, include a sketch of the craft and write a statement. So a quick sketch in which were centered at 66? Well, we have a standard deviation of 2.5. I want to find the probability that an individual is completed 65 inches and 69 inches. So this shaded region I can use my normal CDF command here. My calculator, my lower bound in this case would be 65 my upper bound would be 69. Um, I mean 66 with a 2.5 standard deviation I don't get an area of point 5404 I see. Would you expect to meet many Asian adult males over 72 inches? Explain why, Why not justify your answer? Well, we want to figure out what is the probability that an Asian adult male is over 72 inches. So using the same type of space above where we have a center of 66 and the standard deviation 2.5. We know that 72 somewhere over here, to the right shaded regions to write. So based on the picture, we know that the probability is small, but let's determine how small it is we can use. Our normal CDF demand, which were lower bound, is where we started to shade, which is 72. This goes to infinity, so even represent that with 999 we have a mean of 66 a standard deviation of 2.5. We get the probability of 0.8 So would you expect to me mediation adult males over 72 inches? To my way of saying no sense, the probability of an Asian adult male being taller? 72 inches. It is very low, and I'll share the prince ese and the probability

This problem is about the seat with on Southwest airline flights, and we're given some information. So I recommend starting by writing out what you know what is given to you and in this particular one were given that men's hip breaths are normally distributed. You were also given that the average man's hip breath is 14.4 inches and the standard deviation of that population is 1.0 inches. And in part a, you are asked to determine if a single man is randomly selected. What's the probability that his hip breath is greater than 17 inches? Because they told you about the normal distribution? We're going to draw ourselves a bell curve. We're gonna put the average in the center of that bell to get an image of what's going on, and we want the probability of being greater than 17. So we will need Z scores to solve this and to refresh your memory. The formula for a Z score is X minus mu over sigma, so we want the Z score for 17. So we're going to do 17 minus 14.4 over 1.0, and our Z score turns out to be 2.6. Now. I like to always put our Z score onto our picture, so we're gonna have to 0.6 here. So when we're talking about being ah ah, hip breath greater than 17 we're also talking about having a Z score greater than 2.6. Now, if you go to the table in the back of your book table A two, which is your standard normal table, the table is designed to talk about areas or probabilities that extend into the left tail of the bell curve. And as you can see, our picture is extending into the right tail. So in order to handle that, we're going to have to rewrite our probability statement to read one, minus the probability that Z is less than 2.6. When you look up 2.6 in the table, you will find an area or a probability off 0.9953 And when you subtract that from one, we get an overall probability of 10.47 So recapping part A. The probability that one randomly selected man has a hip breath that is greater than 17. This 0.47 in Part B. We're going to select a sample from the flight, and that sample is going to have a sample size of 122 passengers, and you are asked to determine if the plane is full with 122 randomly selected man Herman. What's the probability that they're mean? Hip breath is greater than 17? And in order to tackle this, we are going to have to determine the average of our sample needs and the standard deviation of our sample means, and we're going to use the central limit the room to determine these two statistics. The Central Limit Theorem says that the average of the sample means is equivalent to the average of your population, and in this case it was 14.4. And the standard deviation of our sample means what equal the standard deviation of our population divided by the square root of our sample size. So in this case, it's going to be 1.0, divided by the square root of 122. Again we're going to draw are bell shaped curve. We're going to put this average in the center, and we're trying to determine the probability that the average is greater than 17. In doing so, we are going to have to use the Z score formula, but there's going to be a slight modification on it because we are working with sample means. So we're going to use e equals X bar minus the average of our sample means over the standard deviation of our sample needs. So in this instance, Z equals 17 minus 14.4 divided by we're going to use this expression as the value for the standard deviation of our sample meat. When you calculate this out, the Z score ends up being 28.72 Yes, it is very ugly. I like to take that Z score and put it back onto our picture, so we have a 28.72 So when we're talking about the probability that the average was greater than 17 it's no different than talking about the probability that are Z score is greater than 28.72 And just like earlier, when we are dealing with the standard normal table in the back of the textbook, the standard normal table goes into your left tail are pictures going into the right tail. So we are going to have to rewrite this as one, minus the probability that C is less than 28 0.72 And when we're looking at that table at the very, very bottom of the positive side, it says that a Z score that is less than 3.5 or greater um, is going to be a 0.9999 So we've got to do one minus 10.9999 and we get 0.1 So again recapping Part B, we're going to select 122 male passengers, and the probability that they're mean hip breath is greater than 17 is going to be 170.1 Now we want to go into part C and in part C. The question is asking you which result should be considered for any changes in seat designs? Should we use part A or part B? And the answer is we should use part a so part A should be used when considering hot seat design changes. And the reason will be because seats are occupied by individual people, not groups of people

Okay, So for this problem will still use the data for doing off mail 68.6 and the standard of imported two point. So, according to you, the problem or part age Hey, so it has adultery. Height. That's equal to 51.6. And we're looking for the percentage that adult men can fit through that high 15.6 without even bending. Okay, so we're actually looking. So since this is 51.6, so we're looking for the area less than 51.6. It's a probability that access less than 51.6. Okay, but we have to standardize this to get the value of Z. Okay, So disease he called to explain this new all over sigma is equal. Thio 51.6, my nurse 68.6 over 2.8. Okay, so calculate the Z score for this one. Hmm. Yeah. Oh, okay. So you must get a value off Z. Mhm. That's equal to negative. Uh, yeah. Oh, active 6.7 Uh, okay. Right. Mhm. So now we're looking for the probability that disease less than negative 6.7 and since the standard normal Kerr happens to be from, uh, negatively three. Then the probabilities is actually equal to zero. Hey there for no men can pass through that door without them. So they have to bend first in order to bash through it. Uh huh. So So, yeah, the door design is actually adequate. So this is adequate. Yeah. The 51.6 is interest. It's actually add it because it will consume a lot off space in the job if if the door high iss, you know, higher. Okay. So, yeah, it's just good to have. It's just good to have a door height that a minimal Yeah, in order to avoid, uh, large space for just or, um And then now we're looking for the value of height that could fit 40% without even then Mhm, you know. Oh, let's just call this down. All right? So we're looking for mhm the value of X. Uh huh. We're in 40% fete without many, so this is 40 percent. So we're looking for the value off X. Less than a certain value. Give us an area equal to zero point 40. Okay. Oh, are in terms of the we have the lessons. Z score, Give us an area off 0.4 or 0.40 me. So you look at the Z table. Look at the corresponding Z score given area. That's all too. 0.4. Uh huh. And that Z score is actually negative. 0.25 Yeah. Okay, So in order to get the X value here, Okay, use the formula. Z equals x minus were over sigma. So we have Z. That's still at a 0.25. Okay, is equal to x minus the mean 60.6 or over two point. So multiply 2.8 on both sides of the equation. We have negative 2.5 negative 0.25 times. 2.8 This actually know that there was zero point, so it's equal to X minus 68 0.6. So we add 68.6 on both sides off the creation. Okay. Lets scare the value that's equal to 67 point line. INGE's Hey,

Hi. It's just trying to solve a problem. Number 14 Problem Number 40 is the same givens as Exercise 39 Mrs Whole. Give her class at N question. Multiple choice with exes. A number off on randomly selected correct questions. N. G in the Grade four students in the class where the grade off each citizens is equal to 10 multiplying by the correct answers. Questions. This is a given for the distribution for it's random variable and the question is asking about how can you find the median off G first Mind steeping that, uh, median three x close B This is a property off. The median is equal to a blind by median. Thanks, plus B. If we try to substitute in this equation, we can say that first list the state, the relationship between G and X, where G is equal to then thanks. So here we can find that if we stayed explodes be so a X loss be so here we can find that a is equal to 10 and B is equal to zero. If we substitute here in this equation by a and B, we can find, that's this is the attitude here and with the equation. So Reunion G is equal to 10 withdrawing by regional backs. And here we can find medium. Wilbanks is equal to 8.5. So then Ryan by eight point Frank. So it is 85 this How can we get median on Jake? Ah, question Be which can be, uh it is stating that Ah fine the enter what time or g Until your methods We can't say the same scene here that I q r which in the Inter queer in time. So let's first on calculate the art you are off X friend in bed. You would. So it is student, but pine minus first. What kind? As with so here, early quarter is equal to nine and first floor tile I couldn't giving is equal to eight. So this is equal to one. But why? Using the property's off the core tight. We can say that I like you r a x plus really is equal to a not the blind by like you are X. And by knowing that a is equal to 10 we can say that I like you are off. G is equal to friend Mark O'Brien by i q r x, which is one. So the final answer would be would be that thethirties which is asking about what shape with the probability distribution on jihad. So now we are trying to find this the shape for than your and the very well at G. And first we can ah created the mean off G 20. For this confusion, we can transfer these Ah huh. That space we can use the same property for median to calculate g ah mean for jeering the variable the same property mean off the X plus B is equal to aim at the blind. Why mean of X plus plus B So we can say that a with the blind. Why, I mean off X plus be And we know that e from here we know that is equipped depends to attend Brother Brian by me, Novak. So let's to try to find me no match, which is 76 7.6 plus the road is 76. So let's try to get her mind or find the shame off. Uh, run the variable g by knowing that Ah, sorry about that. This in chi lines. Okay, so food run the very well g mean is equal to 7.6. So let's assume that it is the mean 70 70 76. And the median is equal to 85. So 85 is more than the mean. So here is a median. So his 18 five And by knowing that the median, the mean is never in the median is indicate that the distribution is lift is skewed, since the mean is influenced by the hour lawyers, which have to be very small because I mean, is Lin then? Ah, well, then the median. So the distribution must mean left left, excuse. So here we can say that the distribution is lift. Yeah, it's cute. And this is the shame. And this is the justification for our financing. Thank you.


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