I have 21 reputation here:  But it won't let me get into chat (I only have 19):  Why is this so? Thanks in advance
I have 24 reputation points, but SO chat is still giving me the message "you must have 20 reputation...." Why can't I join the chat?
I need help with STATS homework about normal distribution The distribution of sale price for new MacBook Air’s is approximately normally distributed with a mean of \$800 and a standard deviation of \$70. (a) Mr. Bob plans to spend between $700 \text{ and } $850 on a new Apple MacBook Air. What proportion of the available MacBook Airs can Mr. Bob afford? (b) What is the 90th percentile of computers of this type? (c) Show that a MacBook Air priced at \$1000 would be considered an outlier using the 1.5 × IQR rule. For a, I tried doing 850-700=50 and $\frac{50}{800} = \frac{1}{40}$, for b, I tried $m+(0.5 \times R)/y$ for c, I tried $1.5 \times 700 - 1.5 \times 850$ Was Voldemort allowed to visit Hogsmeade while in school? We know that in order for third-years and up to be allowed to visit the village of Hogsmeade, they must present a form duly signed by their parent or guardian. When Harry’s guardians, the Dursleys, miss their opportunity (!) to sign his, he is not allowed to go to Hogsmeade. Both Cornelius Fudge (as Minister for Magic) and Professor McGonagall (as head of Gryffindor House) refuse to sign the form on his guardians’ behalf—probably at least in part because they think there’s a mad killer on the loose looking for Harry, but also, as McGonagall specifically states, simply because:  “You heard what I said. No form, no visiting the village. That’s the rule. […] The form clearly states that the parent or guardian must give permission.” Prisoner of Azkaban, Bloomsbury/UK paperback, p. 113  Obviously, Tom Riddle did not have any parents or guardians ready to sign his form for him: his mother was dead, his father likely did not even wish to know of his existence, and if he did have a legal guardian at all (I don’t know how orphanages worked in Britain in the 1930s), it was likely to be  (warning: Wikia link) as the matron of Wool’s Orphanage where Riddle grew up. As Mrs. Cole was perfectly Muggle in every way and was never told by Dumbledore—nor, we must assume, by the boy himself—that Riddle was a wizard attending a wizardry school, it seems unlikely in the extreme that she ever signed Riddle’s form to visit Hogsmeade.1 I don’t recall any incidents in the books where Voldemort speaks specifically of him visiting Hogsmeade as a school boy (then again, why would he?); but being content to remain at the castle while his classmates have fun in the village seems quite out of character for him, too. Are there any (canonical) indications whether special provisions were made for orphans with no legal guardians to sign, so that they were allowed to visit Hogsmeade after all? Or, oppositely, whether such cases were played strictly by the book and unguardianed orphans, and thereby Riddle, were not allowed to visit Hogsmeade?    1 One might of course easily envision that Riddle simply Confounded Mrs. Cole to sign the form; but that would lead to detection of underage magic (assuming this was even a thing in 1940). Riddle may of course have forged Mrs. Cole’s signature, but that would be rather likely to be discovered as a forgery, since at least Dumbledore was aware that Mrs. Cole did not know of Riddle’s magical abilities. How to remove specific elements in a numpy array This is by far the weirdest problem I've come across,  My mac can perfectly access internet through safari web browser, but when I tried to do   ping www.google.com   through the terminal, it's requests is being timed out.  None of the other apps are able to reach internet either. Dropbox, Skype, Spotify all showing offline, except the browser itself  I'm guessing something bad with the DNS, but spend 2 hours trying to fix this with no luck When is the new ball due for all forms of cricket? Is there a standard time fixed in Test, ODI and T20 formats of Cricket, when a fielding side captain can ask for a new ball?  If the captain of the fielding side doesn't ask for a new ball, will he be forced to have it mandatorily after a certain point by the match umpires? Using LINQ to concatenate strings What is the most efficient way to write the old-school:  StringBuilder sb = new StringBuilder(); if (strings.Count &gt; 0) {     foreach (string s in strings)     {         sb.Append(s + ", ");     }     sb.Remove(sb.Length - 2, 2); } return sb.ToString();   ...in LINQ? How to make Ethernet work on Android over OTG? Visual Flow: How to set Date field to Null / Blank? Once a post has been edited, you can go into the revision list, and click "View Source".  If a post has not been edited (and I don't have the edit privilege) is there any way to see the raw Markdown?  The reason I ask I because of  - it's impossible to see the source markdown, and how it's different from the rendered Markdown.  Not exactly a huge issue, just curious! When should I use a List vs a LinkedList Why use the 'ref' keyword when passing an object? Proving the total number of subsets of S is equal to $2^n$ Student here! Just reading Liebecks Introduction to pure mathematics for fun and I made an attempt at proving the total number of subsets of S is equal to $2^n$.   I realized that the total number of subsets of S is just:  $ \binom{n}{1} + \binom{n}{2} + \cdots + \binom{n}{n} + 1$  And so I put together the cool looking formula  $ \displaystyle \sum_{r=1}^n \frac{n!}{r!(n-r)!} = 2^n - 1$  But I have no clue how to approach proving this formula analytically. Any help?    So if I try a proof by induction:  $\displaystyle \sum_{r=1}^n \frac{n!}{r!(n-r)!} = 2^n - 1$  $\displaystyle \sum_{r=0}^n \frac{n!}{r!(n-r)!} = 2^n$  obviously true for $n = 1$:  $1 + \frac{1}{1!0!} = 2 = 2$  assume true for $n$, I could multiply both sides by $2$?  $\displaystyle 2\sum_{r=0}^n \frac{n!}{r!(n-r)!} = 2^{n+1}$  How could I go about proving that  $\displaystyle 2\sum_{r=0}^n \frac{n!}{r!(n-r)!}  = \sum_{r=0}^{n+1} \frac{(n+1)!}{r!((n+1) - r)!}$ How many ordered pairs $(A,B)$ they are if $A$ and $B$ are subsets of $\{ 1,2,3,4,5 \}$ such that $A \cap B = \{1\}$? How many ordered pairs $(A,B)$ they are if $A$ and $B$ are subsets of $\{ 1,2,3,4,5 \}$ such that $A \cap B = \{1\}$?  If 1 is in both sets :  Size of $A$ is $&gt;1$ and size of $B$ is $&gt;1$.  $\Rightarrow$ Size of $A \cup B =4$  $$5 \cdot (3 \cdot 3 \cdot 3 \cdot 3) = 405$$ is not correct.  What am I missing here? How should one interpret the comparison of means from different sample sizes? Take the case of book ratings on a website. Book A is rated by 10,000 people with an average rating of 4.25 and the variance $\sigma = 0.5$. Similarly Book B is rated by 100 people and has a rating of 4.5 with $\sigma = 0.25$.   Now because of the large sample size of Book A the 'mean stabilized' to 4.25. Now for 100 people, it may be that if more people read Book B the mean rating may fall to 4 or 4.25.   how should one interpret the comparison of means from different samples and what are the best conclusions one can/should draw?    For example - can we really say Book B is better than Book A. What is the significance of Lie groups $SO(3)$ and $SU(2)$ to particle physics? I was hoping someone could give an overview as to how the Lie groups $SO(3)$ and $SU(2)$ and their representations can be applied to describe particle physics?  The application of Lie groups and their representations is an enormous field, with vast implications for physics with respect to such things as unification, but I what specifically made these groups of physical importance and why there study is useful.  I have just started studying these two groups in particular, but from a mathematical perspective, I'd very much appreciate understanding some sort of physical motivation. There is a socket related function call in my code, that function is from another module thus out of my control, the problem is that it blocks for hours occasionally, which is totally unacceptable, How can I limit the function execution time from my code? I guess the solution must utilize another thread. Probability question with interarrival times (Why did the chicken cross the road?) A chicken wants to cross a single-lane road where the cars arrive according to a Poisson process with rate $\lambda$. She needs at least $k$ minutes to cross the road safely, so she will have to wait until she sees a gap of at least $k$ between the oncoming cars. If the gap between the car that just arrived and the next one is at least $k$ then she starts crossing the road immediately. Let $T$ denote the random time she needs to wait by the road.  Find the expected time needed to cross the road. My advisor wants me to include a name of someone who has no contribution to the paper My first advisor wants me to include my second advisor's name in a paper that I worked on before she (2nd advisor) came along.   Should I include her name even though she didn't do anything in that paper? I don't think she even read it. How to grep a specific line _and_ the first line of a file? Viruses at this period of time do not fit the current definition of life.   Much of the reasoning behind this is that we currently believe that all life must be made up of cells.  Also, many biologist/scientists say that viruses are not living because all they are is just chemicals carrying out their predefined chemistry.   Has anyone every considered the fact that cells, the supposed building blocks of life, themselves simply only carry out predefined chemical actions? All actions cells carry out are chemically driven, not consciously or spiritually driven. Cells do not make choices, they follow chemical directions present in their DNA and RNA. Viruses act very similarly, following the action transcribed in their DNA or RNA.   How can we really even draw a defined line of what life is?