An airline estimates that 98% of people booked on their flights actually show up. If the airline books 77 people on a flight for which the maximum number is 74, what is the probability that the number of people who show up will exceed the capacity of the plane?
+1036 Use the cumulative binomial distribution function.
\(\hspace{1pt} \ \Pr \left({X \leq 74}\right)=\\ \ 1- \binom { 77} { 75} {0.98}^{ 75} \left({0.02}\right)^{2} + \binom { 77} { 76} {0.98}^{ 76} \left({0. 01}\right)^{1} + \binom { 77} { 77} {0.98}^{ 77} \left({0.02}\right)^{0} \\ \)
I assume you have the brain to crunch the numbers.
+118673
Well, it would be a good answer Nauseated IF you added some brackets. And IF you were wearing your glasses. 
Would you like to borrow mine?
An airline estimates that 98% of people booked on their flights actually show up. If the airline books 77 people on a flight for which the maximum number is 74, what is the probability that the number of people who show up will exceed the capacity of the plane?
P(too many people show up )
= P(75 turn up)+P(76 turn up)+P(77turn up)
\(=^{77}C_{75}(0.98^{75}*0.02^2) +^ {77}C_{76}(0.98^{76}*0.02^1) + ^{77}C_{77}*(0.98^{77}*0.02^0)\\ =^{77}C_{75}(0.98^{75}*0.02^2) +^ {77}C_{76}(0.98^{76}*0.02) + 0.98^{77}\\\)
+1036 Some CDD here:
The answer above gives the probablity they will all have a seat.
The question is:
what is the probability that the number of people who show up will exceed the capacity of the plane?
\(\ \Pr \left({X \gt 74}\right)=\\ \)
In this case do not subtract CDF solution value from 1
+1036 Melody is quick and on the ball.
It’s true. Trolls are not just a little hard of hearing, they have diminished vision too. It’s a symptom of CDD :)
I added some “grace” brackets. Hierarchy is fairly clear on this. Why does it need more?
OK calculate this:
What is the probabilty I could have posted my correction at least 5 seconds sooner?
Arthritis is a royal bítch :)
+1036 ---
There is nothing like a whinging, CDD afflicted, blind, arthritic, old Troll.
Yes. Tis true, we are a very rare breed. But whining? Bítching maybe, but not whining.
Also where do I need the brackets? IF you tell me, that will give me something better to bítch about.
Yalls conversation is funny!lol I like melodies part of the conversation better... Y'all are good at trash talking😀
+1036 Yes, guest that is true.
I’ll tell you a secret why Melody is so good at it. Melody is a genetically modified ancient (dinosaur era) troll made to look human. She fools almost everyone except other trolls.
Morgan le’Fay did the DNA modification about 900 years ago.
Ain't Morgan le fay like King Arthur and the Knights of the round table era. Ya could say someone real instead such as: Archemedes, Isaac Newton, Plato, or anyone else real, but long gone.😀
+118673 Whinging may not be the right word but neither is bitching!
Maybe we interpret the 2 words slightly differently from one another ://
I was actually surprised because your normal recourse is to blame the poster and say that their question was ambiguous.
Usually you accept zero blame for your wrong answers. 
"Also where do I need the brackets?"
P(not too many people) = 1- (prob of too many people) = 1- [ P(75 turn up)+P(76 turn up)+P(77turn up) ]
NOTE:
Nauseated often rubs me the wrong way and it is good when I can get a little of my own back BUT we are actually quite fond of one another :)
I can tell, ya only tease people ya like.😀 I do the same thing though my friends usually get offended when we make trash talking championship, they can't seem to find any good ones, while I hav a surplus of good ones in reserve...
+1036 I was actually surprised because your normal recourse is to blame the poster and say that their question was ambiguous.---
The reason that is normal is because it normally true. The questions are ambiguous. I get to guess which arbitrary path to take, and then you take the other path and tell me my brilliant answer is wrong. See . . . she is a skilled troll.
**Usually you accept zero blame for your wrong answers. cheeky***
I’ve posted one wrong answer on here. That was a correction to a post where the original answer was correct.
"Also where do I need the brackets?"
P(not too many people) = 1- (prob of too many people) = 1- [ P(75 turn up)+P(76 turn up)+P(77turn up) ]
That was your equation form, not mine. Mine was neat and orderly, so it didn’t need those brackets.
NOTE:
Nauseated often rubs me the wrong way and it is good when I can get a little of my own back BUT we are actually quite fond of one another :)
Yes. We are. She is the only troll on here who can keep up with me. I still really píss her off, though. ROFLOL
+118673 No,no, no,
If such a modification was conducted it would indeed have been by Morgan le’Fay.
This used to be the realm of Camelot. It was Nauseated himself who dethroned the Queen so he would know.
The Queen has been waiting in exile for some time now for her subjects to rally and reimpose her reign.
Occasionally she sees TitaniumRome and she wonders if he will take up arms on her behalf but then he disappeasrs into the mist again.
Now DragonSlayer554 is back perhaps he can rally some troups.....
She often wonders if Morgan Tud will help, he could partition Morgan le'Fay to caste a spell over the realm's tyrant. It is Nauseated of whom I speak of course but Tud has a great love affair with his bottle and The Queen thinks that his loyalty to the throne has wavered.
By his words here it seems that Nauseated may even prefered the rule of Queen Guinevere to the present chaos that assaults this fine land.
I just fell over laughing! That was really good Shakespeare. You just moved ahead of nauseated 6 points.
+118673 "That was your equation form, not mine. Mine was neat and orderly, so it didn’t need those brackets. "
See Nauseated rarely admits when his answers are garbage.
He will argue that his wrong answers are correct until he is blue in the face.
Nauseated, you do need those brackets - I expect you already know that, but you would not want to lose MORE face would you!
Nauseated and I must be similar. "There is no such thing as defeat..." Man I wish I had music to play with that line... Imagine Mozart banging on the piano.😀
Where didst thou get thoust pic. I findest it amusing... Man writing in Shakespearean English is hard!😀
+1036 You were never dethroned and your exile seems self-imposed. All your knights are here – even Rom returned from the sea. Princess Kitty is on sabbatical, but she visits on occasion. The Ghost logged on a few days ago. Morgan Tud is sailing the seas – probably trying to find some good rum. Sir CPhill is still pushing the bolder up the hill.
Many of your subjects came in with the wind and left the same way. They may yet return when the wind changes again. .
But your favorite Troll is ever faithful . . . . :)
Over all, your kingdom seems well, just different with the passage of time.
+118673 I still really píss her off, though. ROFLOL
Yes that is true but I really p*** him off too. He is too full of unjustified pride to ever admit it though!
If you want to use italics guest you just highlight the words and press the I button on the ribbon. :)
What time is it in Sydney ( that is where yo said yo lived right) most people in my time are asleep. Unless there at a bar then they might be still awake.😀
+118673 Well Nauseated I seem to have hit a raw nerve!
Were you adressing me or were you adressing the Queen?
If it be the Queen that you be addresssing than you take great liberties.
It is totally improper for the Queen to be address with such blatant familiarity!
And from a mere surf to. Tut, tut, tut.....
Y'all are so funny!!!!!!!! Yo should start a talk show.😀 lol I would pay money to see that.
+118673 It is Tuesday 8:20 pm in Sydney at the present time.
We in Australia are in front of most of the World. We are certainly infront of Nauseated's dank cave. He lives under a toll bridge you know. There are many toll bridges on our little Jiang. Yes, I know, trolls do not usually live in China but this is an international forum and we have multicultural trolls. They all live in dank, dark, stinky places though. That is how they like it best. They usually only emerge to demand fees and reak havoc on unsuspecting travelers as the later attempt to cross the troll's ricketty bridge. ://
Poor you it is so late over there it is 3:33 am Tuesday morning.
i wonder if nauseating has a friend under her bridge
+118673 Yes well, Nauseated sure needs a 'friend' of the female gender.
That is most probably his main problem.
You see finding a mate makes a troll mellow and mellow trolls are not attractive to other trolls.
That is why the world is not over run with little trolls.
It is quite sad really - a major genetic failing within the species.
+1036 It may be improper for a humanoid subject to address the queen in such a manner, but I am a troll with K-9 DNA. Remember the dogs of the royal house have free reign of the castle and lounge wherever they desire – including the royal bed. BTW there are a lot of fleas there. :)
--------------
Guest, your score-keeping sụcks!
How do y'all even come up with this stuff? Is it rehearsed? How old are you melody? Sometimes yo seem older sometimes yo seem younger.
Don't worry nauseated I just bumped you up 5 points for that comment.😀 Keep up the good work.
+118673 Some self important person once told me that like attracts like so it does not surprise me that when you move into the Queens bed you bring the other vermin with you. I also know for a fact that the Queen never sleeps in the same bed 2 nights running. For her majesty, a new night means a new bed and the vermin do not move in until the following day. LOL
Her majesty never shares her bed with parasites!
+118673 Your judging skills were just fine until you gave Nauseated 5 more points!
You should be careful, you do not want to bring on the wraith of Queen Guinevere.
Now that Nauseated has admitted that life without her is not worth living !!
I think she may choose to return and she will want her subjects to see her power!
I wish I had your imagination.☺️ I hav nil imagination. Unless inputs a fantasy land with the characters in my books.
I liked her comment. What did yo want me to do lie p. I guess yo aren't gonna tell me your age?
+1036
>No one really knows how old Melody is, but she use to have a tyrannosaurus rex as a pet.
>This is impromptu trolling. We are professionals. Well I am, Melody is just a ranking amateur.
How is it fair to say my judging skills suck? I just call it like I see it.
>It’s fair, because I call it like I see it.
She has to be kindve older I'd think since she used to be a teacher or still is and no younger person is smart enough to answer all those questions?But she can't be that old cause I don't bore of listening to her. But I guess she can stay illusive if she wants its always fun to act mysteirious.
Dear Nausested,
Why do you nauseate me so?
Why do you always have a corky response to which I cannot reply?
I know I'm bad at poetry but I thought I'd give it a try that is as far as I got.
+1036 Guest: Melody’s comments are just obiter dictum. Nothing is intended to be a literal criticism. You are simply part of the game. Now if you post a math solution and demonstrate CDD then my trolling is serious business.
---
There are many posts where Melody and I deliver witty repartee. Our best one hit critical mass and became thermonuclear. I still have radiation burns.
+45 The Queen hath been awaken from Her Royal slumber.
She sees the vermin Nauseated is still within the realm.
Fetch the Good Doctor, the Queen needeth the physicians healing hands.
She also seeks his excessively ingratiating graces.
Go knave, search high and low and bring the physician upon this fair day !
A thought before you go, add some salt to this request - tell him there be 20 barrels of rum in the Royal cellar.
His if he be here within the day. And another barrel for you my knave - Bring forth Chiurgeon Morgan Tud !!
I know that but it bothers me when I can't think of a response. And yes I also knew I was just your play toy, but I like being a puppet. I do this in a lot of people's posts...😜
Nauseated: you never told me if you liked my Barney, All About that Base, and Cool Kids parodies😔
+45 Are you still here my knave. Be off with you and return henceforth with Chiurgeon Tud in tow!
+118673 Who is ignoring you?
No one would dare ignore the Queen !!
Not if she has truly been returned to power! :///
+1036 Why do you nauseate me so?
The answer is easy:
I may be nauseating to others because nausea is sympathetically induced when one is exposed to another who is experiencing the effect. The rate is about the same as a yawn. BTW: I call myself Nauseated because I’m nauseated by CDD and related disorders in others.
And yes I also knew I was just your play toy, but I like being a puppet.
You are not a puppet. You are an interactive participant. You may be an audience of one but you are a catalyst to our repartee.
+118673 Yes, this thread would have wound up long ago if we did not have you as a participating audience.
So thank you 
Dear nauseated I speak English, so I am not sure if that was an insult or a compliment but I am touched either way.😀 lol
ps: did I forget to mention that I was just looking for something that sort of rhymed.
also did yo look at my parodies?!?!?!?!?!?!???????!!!!!!!!!!!?!?!?!?!
I know melody I am amazing. Lol. It is the reason I interrupt people's posts, I like long ones,😜😜
Ohhhhhhhhh so that's what a thread is. I had no idea what people were talking about when they said threads.😀
+45 Knave, thee still be here? Where be the Good Doctor !
The Chiurgeon presented The Queen with a wondrous gift one time.
"The magick of the Quadratic!" He be an enchanted Chiurgeon.
Perhaps Morgan LeFaye helped with the charm :/
They be a powerful duo!
Dear queen quenivere my modern self has a very hard time understanding Ye old English. Lol
+163 Aye, Your Majesty, I be at thy call in an instant and that be well less than a week where I be.
My eyes do always wonder at the crystal sphere which beckons at the behest of Your Majesty, or the Royal Princess, and the royal mutt, too. There be only one other who calleth me on this sphere, and I pray she not appear in any form. Her name be Morgan . . .
How may I serve thee?
M-1
+45 Thank you knave. The Queen sees the good Doctor on the horizon.
The Queen be so excited. In a reserved kind of way - thee must observe!!
Here be thine payment. Thou expedience will not be forgotten too readily!
+163 Aye, Your majesty. Many thanks to thee and your royal house. It be exceeding rare that I be paid before service is rendered.
I have beheld the dialogues and it seemeth the royal mutt is more nauseous than be his norm. Hath he delivered vomit on the floor of thy royal palace?
Perhaps a tonic he needeth?
+163 I be a churgeon of the medical arts.
Of whom be ye? Be thee a subject of her majesty? Or be thee a visitor from a far away land?
+45 Why Chuigeon Tud, cannot the Queen of the magical realm of Camelot call thee forth without an alterior motive.
I have mislaid thine great gift. Can thee use thine enchanted Crystal sphere to uncover the whereabout of the Queen's "Majick of the quadratic" The Queen hath looked under her bed but since the Queen lays in a new resting place each night it was not there!
It is so good to see you Chiurgeon, it has been such a long time. The Queen was in exile for the longest time.... The nasty troll Nauesated banished her from the realm but now Nauseated laments - he sees the foolishness of his ways and begs the Queen's return. What says your Crystal Sphere? Is the magical realm of Camelot ready for the Queen's return?
+45 The Queen be doubly important but that does not mean her posts must multiply. !!
+163 cannot the Queen of the magical realm of Camelot call thee forth without an alterior motive
Aye! Her majesty may do as her majesty pleaseth. There be none who contradicteth thee.
Here be that which thee bid me to findeth.
+45 "Aye, Your majesty. Many thanks to thee and your royal house. It be exceeding rare that I be paid before service is rendered".
No, no, no thou hath misunderstood.
That barrel be payment for the knaves service. Thou hath not been paid yet!
Here be your payment! I trust it is to you liking my dear Doctor.
I have beheld the dialogues and it seemeth the royal mutt is more nauseous than be his norm. Hath he delivered vomit on the floor of thy royal palace?
Yes the Royal mutt AND his fleas be more nauseating - I mean nauseous than usual. He likes to knaw on decaying vermon. This be his problem. The rest of the realm just has to adjust to the unpleasant consequences. The Queen is thinking of terminating this pet. Perhaps a maltese terrier, one with good manners, may be more to Her liking. But then, there is something about Nauseated..... He has ATTITUDE!
Perhaps a tonic he needeth? He needeth mouth wash, this be a FACT!
Maybe a tonic, but The Queen is not so sure she wants to nurse him back to his full repugnance! ://
Hath thee found the Queen's Quadratic yet?
+1036 Oh no! I went to feed my pet vultures. On my I return I find the doctor of quackery at hand. I have a pet duck and he does not quack properly, maybe you can help.
+163 Aye, Your majesty, that is a royal payment indeed!
I have made a find of the magick-of-the-quadratic and the map of its place be on the first post above thy post.
+45 Thank you my good Churgeon for finding my "Magick of the Quadratic" I do love this gift so much!
http://web2.0calc.com/questions/magick-of-the-quadratic
Oh no! I went to feed my pet vultures. On my I return I find the doctor of quackery at hand. I have a pet duck and he does not quack properly, maybe you can help.
See what Camelot has to put up with from Nauseated! That mutt has no respect for anyone or anything. See how he speaks of you, esteemed Churgeon Tud. The Queen offers Her deepest appologies on behalf of all Camelot, she also is again considering terminating the Mutt. The reason the duck does not quack properly is that Nauseated terminated it! Not even a Great Chiurgeon can cure death! Poor duck
+163
See what Camelot has to put up with from Nauseated! That mutt has no respect for anyone or anything.
He doeth seem to bite often, but he doest not maul. A strange troll dog to behold for sure.
His duck may yet be alive, but perhaps the vapors of his breath take that of the duck to the aether. Holdest thy breath Nauseated when thee be near thy duck and the quacking may returneth.
+45 The Queen thinks she shall now retire.
Thankyou for your prompt attendance. The knave will help you with your Rum.
Do not be a stranger to Camelot. We have many people of ill health here. Just the other day and aging serf went upon his roof. He is rather crotchedly so a rope he tied around himself. Tis just as well or down he may have fell. He carried a great sledge hammer to fix some slipping thatch. A smaller hammer would have done the job but his eyesight is failing and he did not want to loose the sight of it. Down upon his finger he slambed the sledge! Poor fellow, his hand is the size of a football. Could thou please attend him before you leave the realm? Also please inform him that such activity is not appropriate at his advancing age.
Untill next time Churgeon Tud. I bid thee adieu :)
The Queen sees your advice to Nauseated regarding his Duck. You may be right, you are very wise. Nauseated breath could k**l a komodo Dragon! The poor duck would have no chance. Poor Duck. What a way to go.
+163 Thee are most welcome your Majesty.
To thee your Majesty, for the gift of rum, I thank thee. I shall never be in want again.
This surf ye speak of, there be another I attendeth to not a week ago thence, he be like the one ye speak of except it be his foot the mallet landeth up on. He be greatful it not be an ax he swingeth.
In thy service always
Morgan Tud
M-1
