Transcript
0:00calculator
0:01It is said that techniques for probabilities
0:03Problems
0:03That it is possible
0:05Exit the
0:06Engineering Board exams
0:07And for the part one of two of our caltech
0:10Video for probability
0:12This is what we will try
0:14Problem
0:15Let's wrap that up
0:18Pak pak pakak
0:19My name is
0:20calculus b
0:21Your tiktok
0:22Calculus baby
0:24Light bulbs
0:25Having a meaning
0:25Life of two thousand four hundred hours and a standard
0:28Deviation of Sixty
0:29Two hours
0:30They are used for a constant consignment of four thousand
0:33bulbs
0:34Determines the percentage of bulbs with a life
0:37Between two thousand three hundred and two thousand
0:40Five hundred hours
0:42So new
0:42Dealing with the problem and with
0:44The caltech
0:45necessary
0:45Let's first understand how to work
0:48Normal distribution
0:49Actually this is an
0:50Examples of
0:52As normal
0:52distribution
0:53Problem even though he didn't say it was normal
0:55He is distribution
0:57Because we can expect that
1:00As yours
1:00Life span
1:01A life bulb
1:02It is normally distributed
1:05Okay let's say you have a random variable
1:10Normally distributed
1:12Notation
1:13With meaning mu
1:16And Sigma
1:17So this is for the population
1:19So yours
1:19Probability
1:21That's your x
1:22Will fall between a and b
1:25This is the area between um
1:28Between
1:29Some curves
1:30Okay so let's say this is yours
1:32Your x axis
1:33This is your a
1:35This is your b
1:36So is meaning
1:36Your curve
1:38In your normal
1:39Probability distribution or your bell curve
1:42That we call
1:44So this probability is
1:46Given by
1:48By this area
1:50And you can actually compute this
1:52Area when you know the probability
1:55Function of
1:58So if we are not using
2:00As caltech here
2:01It will be
2:02The formula is from a to b
2:05Integral of
2:06One over squirt of
2:09Two pi
2:10And then Sigma which is the
2:13Standard deviation of the population
2:15Times e
2:16Raised to negative one half
2:19x minus the mean
2:21Over Sigma Square
2:25Isn't it unhugarded?
2:28And if you have heard that the actual z score
2:31Others are compiled to using the standard
2:35What you are doing is you are posting z
2:38equal to
2:39The x minus mu
2:41Over Sigma
2:43Then they compute the ones
2:46One over
2:47Sheep squirot
2:49erase two
2:50negative one half
2:52z square
2:54d z then here are the z scores
2:57No here are your exes you just make them z
3:00So z one z two
3:04Where is z one mo z one is
3:07Your first x is a
3:09Minus mu over sigma
3:12Then z two is
3:14b minus mu
3:18So without caltech
3:20We can answer this problem in two ways
3:22Because you can think about that
3:24The percentage
3:24Of bulbs with the lifespan
3:26Between two thousand three hundred and
3:28Two thousand five hundred hours
3:30As the probability
3:32That's the lifespan
3:33Of a
3:35ah light bulb
3:36It is between two thousand
3:37Three hundred and two thousand five hundred
3:39And that's here in x no so this is method one
3:44Then we will fiddle later I will show
3:46We need to understand because before flipping
3:49So the probability
3:52Between two three
3:56And two five
3:58It is equal to the integral
4:00From two three
4:01To two five
4:03Of one over
4:04Square root
4:05Of two pi
4:06Your done
4:07Sigma mo here
4:08Is the standard deviation which is
4:11Sixty two
4:13Times e raised to negative one half
4:16Then x
4:17Minus the means
4:19Population mean
4:20Two thousand four hundred
4:25Square dx no
4:27Then what comes out here in calcu
4:29That will be the answer
4:31So I put him in calcu
4:33Let's see what comes out
4:35Answer here
4:37The answer that will appear should be one of the ones here
4:40So he lasted quite a while
4:42Because we don't tick
4:44okay zero points
4:46Eight nine three
4:48Two something
4:49Something or
4:50Eighty nine points thirty two
4:53percent
4:54I'll actually see you right away,
4:56letter b
4:57But the disadvantage of this
4:58The method is you have to
5:00You have to memorize this and you have to
5:02Integrated
5:04Without caltech
5:05We actually just substituted on zz
5:08All your exes are integral we will make z
5:11Okay so let's do that without caltech first
5:14And then later
5:15The one with
5:16caltech
5:17It's okay with the method
5:18This is what we will do in caltech
5:21The probability is okay
5:24Your ex is from two thousand
5:26Three hundred
5:28Up to two thousand five hundred is equal to
5:31The probability that
5:34Your z is
5:35Between something to something
5:37Okay here is the z one
5:39z two is here
5:41Okay so what is our z one
5:43z one of ours is icoconvert
5:45Mo to
5:47To z
5:48Which is used
5:49Formula x minus
5:50Mu over Sigma
5:52So our x here is two thousand three hundred
5:56Minus our mu
6:00Two fours
6:03All over
6:05Sigma the Sigma is Sixty
6:08Two
6:11The same is what we will do with one to get z two
6:14z two is x minus me over sigma
6:16So two five minus
6:19Two fours all over
6:20And you should get
6:22What the heck is this
6:24Fifty over
6:26Thirty ones
6:28So standardized
6:29We are normal
6:30What we will use
6:31Here goes from z one to z two and then dysfunction
6:36So I just wrote down the values
6:39z one is ours here
6:41And z two
6:44I entered the
6:45We but our variable here x
6:48No it doesn't matter because it's a dummy
6:50variable variable
6:53It needs to be the same as before
6:56Okay so no point
7:01Eight nine three two
7:03Or eighty nine points thirty two
7:08So the question now is how to tick
7:11All you can think of here is this
7:13Integral
7:15So the first thing you should do is
7:17These x mos here is to convert to z
7:21So you need it
7:25So when it comes
7:27In caltech
7:29That probability
7:31From
7:32Negative Fifty Over
7:36The one is up to fifty over thirty
7:39Because you have what is his standard
7:40So normal z
7:41What he has
7:43Okay though
7:44Be careful
7:44Let's go to
7:46Because the
7:47Recalculated by
7:48Your calculator when you start mode
7:50Supposedly three
7:51Then you choose
7:54Start mode
7:57He is actually the p
7:58Will
7:59He entered you with a number
8:00What is that number?
8:02So let's say this is the bell
8:04Your curve is standard
8:05So normal
8:07You enter a number there
8:09Supposedly you let a in here
8:11What your calcu will give you is this area
8:15But what we are talking about here is
8:17Area between
8:18Negative Fifty
8:19To thirty ones then fifty
8:21To thirty ones
8:22So metric is the standard
8:24Our normal at zero
8:26This is the area we are looking for
8:29It's okay if it's scaltech
8:30That's your interest in calcu is
8:34So is the first one
8:37The one in
8:38He will give its place thirty ones
8:41That's it
8:46He will give the one
8:48Its area
8:49So with our caltech
8:52What you enter should be
8:55Fifty over thirty ones are like this
8:57Its area minus
9:00Area of in negative fifty over
9:02Thirty ones so you can get the one in the middle
9:06Let's enter the
9:07To so start
9:08We are in shift mode
9:10Starting
9:12p
9:13Of
9:18Shipping Store to a
9:20And then here it is
9:24distribution one
9:30And then shift
9:31Store to b
9:33Then calculate
9:34c a minus b
9:36So you have zero point eight nine three two something
9:39Something or eighty nine
9:41Point thirty two something something
9:45Which is
9:48Almost the same as that
9:50That's the actual
9:52It's our competition when you flip
Mind Map
Loading mind map…
Viral Breakdown
Hook (first 3 seconds)
- Verbatim opening: "It is said that techniques for probabilities Problems That it is possible Exit the Engineering Board exams"
- Hook pattern: Bold claim + authority challenge ("it is possible to exit the Engineering Board exams")
- Why it stops scroll: It promises a "hack" (caltech) to bypass a notoriously difficult exam section, targeting a specific high-stakes audience (engineering students) with an implicit "you don't need to suffer" payoff.
Emotional Rhythm
- Curiosity/Intrigue: The bold claim about exam-passing techniques (0–5s)
- Tension/Setup: Problem presented with specific numbers (mean 2400, SD 62) — viewer braces for complex math
- Relief/Validation: Creator acknowledges "this is actually a normal distribution problem" — makes it feel manageable
- Suspense Build: Walks through the "ugly" integral formula — viewer fears the worst
- Twist/Payoff: "Let's see what comes out" — calculator reveals answer instantly (0.8932)
- Climax: "Eighty-nine point thirty-two percent... letter b" — the hack delivers, instant gratification
- Resolution/Reinforcement: Shows the caltech shortcut method, ending with "That's the actual competition when you flip"
Climax moment: The calculator output revealing "0.8932" — the moment the "impossible" problem collapses into one keystroke.
Keyword Density
- "Caltech" (calculator technique) — drives search/algorithmic reach; unique niche term
- "Probability" — high-volume academic keyword; algorithmic reach
- "Normal distribution" — core concept; educational search traffic
- "Z-score" / "z" — technical term; signals credibility to the niche
- "Engineering Board exams" — high-stakes aspirational keyword; emotional pull
- "Percentage" — outcome-oriented; tells viewers the answer format
- "Standard deviation" — authority signal; educational depth
- "Integral" — pain point word; emotional pull (viewers fear this)
Algorithmic drivers: "Caltech," "probability," "Engineering Board exams" — searchable, niche-specific, high-intent.
Emotional pull: "Board exams," "integral," "standard deviation" — trigger fear/relief cycles.
Why It Spreads
- "Hack" promise delivered visibly: The creator actually presses buttons on a calculator and shows the answer appear — proof, not theory. The line "Let's see what comes out" is the trust-building moment.
- Fear-to-relief arc: The "ugly" integral formula ("Isn't it unhugarded?") creates dread, then the caltech shortcut dissolves it. Viewers share this as "I survived this — here's the easy way."
- Exam-specific stakes: "Engineering Board exams" is a massive, anxious community. The video gives a concrete, replicable method (mode 3 → shift → store → calculate) that viewers can screenshot and save.
- Clear before/after contrast: Method 1 (integral, "you have to memorize this") vs. Method 2 (caltech, instant). This binary makes the value proposition unmistakable.
- Verbal repetition of key numbers: "Two thousand three hundred," "two thousand five hundred," "sixty-two" — repeated throughout, making the problem feel familiar and solvable, increasing retention.
What You Can Steal
- Open with a "forbidden shortcut" claim: Frame your content as "this is how you bypass the hard way" — even if the method is standard, the framing creates urgency.
- Show the "ugly" version first: Briefly expose the painful/difficult path (the integral) before revealing the shortcut. The contrast makes the hack feel 10x more valuable.
- End with a replicable button-press sequence: Give viewers a step-by-step mechanical action (mode → shift → store → calculate). Specific, repeatable instructions get saved, screenshotted, and shared.
